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  • 1995-1999  (1,288)
  • 1998  (1,288)
  • Engineering  (644)
  • General Chemistry  (643)
  • Nuclear reactions
  • 101
    Electronic Resource
    Electronic Resource
    General approach to automatic generation of quadrilaterals on three-dimensional surfaces (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 609-620 
    Details
    ISSN: 1069-8299
    Keywords: quadrilateral finite-element generation ; three-dimensional surfaces ; CAD/CAM interface ; topological information generation ; node sampling on edges ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, a general approach to automatic generation of quadrilaterals on three-dimensional surfaces is presented. The approach is based on the mapping method for surface meshing and the looping method for generation of quadrilaterals on the mapped plane. Several schemes including a coedge treatment scheme, an allowable tolerance and distance scheme, a multipatch treatment scheme with new mapping functions and a remapping scheme are proposed. Several realistic application examples are given, which show the generality of the presented approach. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 12 Ill.
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  • 102
    Electronic Resource
    Electronic Resource
    A frequency condensation method for the eigenvalue problem (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 1-8 
    Details
    ISSN: 1069-8299
    Keywords: frequency condensation method ; large matrix systems ; Guyan method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A frequency condensation method is presented for solving the eigenvalue problem of a large matrix system. The eigenproblem is reduced to a smaller problem by condensing the stiffness and mass matrices. As distinct from the Guyan method, the frequency condensation method is based on approximation preserving eigenvalues in a preset frequency range and effective procedure of master and slave selection. A numerical example and comparison with subspace iteration and Lanczos methods demonstrate good accuracy and the high performance of this method. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 3 Ill.
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  • 103
    Electronic Resource
    Electronic Resource
    On the discrete conservation of the Gauss-Poisson equation of plasma physics (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 23-34 
    Details
    ISSN: 1069-8299
    Keywords: Gauss-Poisson equation ; exact discrete conservation ; discrete divergence ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We consider numerical methods which exactly preserve the Gauss-Poisson equation when solving the charge conservation and Maxwell-Ampère's equations. Apart from the well-known leap-frog method, we present two situations where this property is verified, one with rectangular mesh and functions defined at the center of the cells, and one with a finite volume type of formulation on triangles. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 4 Ill.
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  • 104
    Electronic Resource
    Electronic Resource
    A user-controlled arc-length method for convergence to predefined deformation states (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 51-58 
    Details
    ISSN: 1069-8299
    Keywords: arc-length method ; user control ; accumulated arc-length control ; non-linear analysis ; predefined deformation states ; convergence ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The arc-length method has been widely used in non-linear analysis of structures. While it can handle complex load-deflection paths effectively, the analyst has no control over the load incrementation scheme to achieve convergence to specific locations along the load-deflection path. There are a number of situations in which such control is necessary, for example when convergence to predefined load levels, displacement levels or stress levels is required. This paper describes an improved arc-length method in which this deficiency is overcome. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 4 Ill.
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  • 105
    Electronic Resource
    Electronic Resource
    Hermitian lumped mass matrix formulation for flexural wave propagation (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 43-49 
    Details
    ISSN: 1069-8299
    Keywords: lumped mass matrix ; Hermitian finite difference operators ; flexural wave propagation ; numeric velocity dispersion ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Hermitian finite difference operators are employed to formulate a new diagonal mass matrix for solving flexural wave propagation problems. The dynamic equilibrium for moments is considered. The consistency of the formulation is evident because these operators explicitly present second-order convergence. Numerical results indicate that the velocity dispersion is very close to the consistent mass matrix. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 2 Ill.
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  • 106
    Electronic Resource
    Electronic Resource
    Reduced-cost methods for large time domain integral equation scattering analyses (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 751-761 
    Details
    ISSN: 1069-8299
    Keywords: acoustic ; electromagnetic ; integral equations ; scattering ; time domain ; radar cross-section ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Analysis of high frequency scattering using pulsed illumination generates surface fields which are small over most of the scatterer most of the time. A reformulation of the usual integral equation time domain approach which exploits this is presented. It is shown that cost scaling can be reduced, with costs reduced by an order of magnitude for the examples presented, with negligible accuracy loss. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 5 Ill.
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  • 107
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    Electronic Resource
    Efficient incompressible flow calculations using PQ2Q1 element (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 161-178 
    Details
    ISSN: 1069-8299
    Keywords: finite elements ; unsteady incompressible flows ; fractional-step ; equal-order-interpolation ; pQ2Q1 element ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Implementation of an equal-order-interpolation velocity-pressure element pair is presented for the finite element solution of incompressible viscous flows. A fractional-step method is employed for temporal discretization. The element pair, also called a pseudo-biquadratic velocity/bilinear pressure element (pQ2Q1), consists of a bilinear pressure element and bilinear velocity elements defined on subdivisions of the pressure element. This pair satisfies the so-called ‘Ladyzhenskaya-Babuska-Brezzi’ condition. Considerable savings in computational cost are achieved due to the reduced number of elements for pressure. A modification of the element is realized for a better representation of curved surfaces. Two test cases, namely the lid-driven cavity flow and impulsively started circular cylinder in cross-flow, are used to assess the accuracy and efficiency of the element compared to a regular bilinear velocity-pressure (Q1Q1) element pair. Computational results presented show that the pQ2Q1 element solutions require less memory and CPU time compared to Q1Q1 element solutions, for at least the same accuracy. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 12 Ill.
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  • 108
    Electronic Resource
    Electronic Resource
    Elastic torsional analysis of prismatic shafts by differential quadrature method (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 195-208 
    Details
    ISSN: 1069-8299
    Keywords: differential quadrature method ; elastic torsion ; numerical solution ; Poisson equation ; Laplace equation ; geometric mapping ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The governing equation of an elastic prismatic shaft is the two-dimensional Poisson equation defined on the cross-sectional area of the shaft. In this paper, the differential quadrature method (DQM) is employed to solve the Poisson equation on some non-rectangular domains. Singularities, which may appear in the expression of stress components or boundary conditions at a degenerated point of the grid, are removed by means of the Taylor expansion. The results of three examples are compared with the exact solutions. It is shown that accurate results can be achieved by the DQM. In addition, three geometric transformations are conducted in the third example so that the effect of mapping on the convergence and accuracy of results is investigated. It is found that rapid convergence can be fulfilled if the degenerated point of the mesh falls on a Dirichlet boundary. The approach addressed in the paper can be extended to other potential problems governed by either the Poisson equation or the Laplace equation. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 5 Ill.
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  • 109
    Electronic Resource
    Electronic Resource
    An explicit fourth-order compact finite difference scheme for three-dimensional convection-diffusion equation (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 209-218 
    Details
    ISSN: 1069-8299
    Keywords: three-dimensional convection-diffusion equation ; fourth-order compact scheme ; iterative methods ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We present an explicit fourth-order compact finite difference scheme for approximating the three-dimensional convection-diffusion equation with variable coefficients. This 19-point formula is defined on a uniform cubic grid. We compare the advantages and implementation costs of the new scheme with the standard 7-point scheme in the context of basic iterative methods. Numerical examples are used to verify the fourth-order convergence rate of the scheme and to show that the Gauss-Seidel iterative method converges for large values of the convection coefficients. Some algebraic properties of the coefficient matrices arising from different discretization schemes are compared. We also comment on the potential use of the fourth-order compact scheme with multilevel iterative methods. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 2 Ill.
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  • 110
    Electronic Resource
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    Finite element analysis of pollutant transport in water-saturated soil (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 241-251 
    Details
    ISSN: 1069-8299
    Keywords: finite elements ; pollutant ; saturated porous medium ; semi-implicit method ; velocity correction ; mass transfer ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A practical problem of pollutant migration has been studied for different concentration differences and mass diffusivities using the finite element method. The results indicate that the pollutant takes years to travel 10 m into the water-saturated soil when the mass diffusivity and concentration differences are less. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 6 Ill.
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  • 111
    Electronic Resource
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    Solution of Stokes equations by moving least squares (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 907-920 
    Details
    ISSN: 1069-8299
    Keywords: Stokes problem ; meshless ; MLS interpolant ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper a numerical solution for incompressible Stokes equations using moving least-squares interpolators is developed. This approach does not require an element discretization; just a cloud of points is necessary. This is very attractive for 3D problems and deformable domains. First, taking into consideration that Dirichlet boundary conditions are not applicable a posteriori as in finite elements, a variational weak formulation that includes all kinematic restrictions (Dirichlet and incompressibility) is derived. Then the discretized resultant equations using a moving least-squares (MLS) interpolant for velocity and pressure fields are presented. Finally, the performance of the MLS interpolation is analysed by comparing numerical and analytical solutions, paying attention to the selection of the polynomial degree for the basis function and its orthogonalization. Different aspects of numerical implementation are discussed. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 6 Ill.
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  • 112
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    Fast-secant algorithms for the non-linear Richards equation (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 921-930 
    Details
    ISSN: 1069-8299
    Keywords: non-linear Richards equation ; mixed-hybrid finite elements ; quasi-Newton methods ; fast-secant methods ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Groundwater flow in partially saturated porous media is modelled by using the non-linear Richards equation, which is discretized in the present work by using linear mixed-hybrid finite elements.The discretization produces an algebraic non-linear system, which can be solved by an iterative fixed-point algorithm, the Picard method. The convergence rate is linear, and may be too poor for practical applications. A superlinear convergence rate is obtained by considering a Broyden-type approach, based on the Shermann-Morrison formula.The local character of the Broyden method can be overcome by an accurate estimate of the initial solution, that is by appropriately initializing the computation via some (relaxed) Picard iterations. This strategy needs a convergence criterion to decide when switching from the Picard to the quasi-Newton method, which is crucial for the effectiveness of the scheme, as illustrated by some numerical experiments.We also consider the non-linear algebraic problem from a different viewpoint. Instead of applying the quasi-Newton method directly to such a non-linear system, we applied it to the non-linear function tied to the Picard scheme. Each function evaluation requested by such an algorithm corresponds to a local step of the Picard method, which is then used to compute a Broyden displacement. The present technique can be seen as an accelerated Picard algorithm.We compare the performances of these algorithms when applied to a stationary and a time-dependent benchmark problem. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 6 Ill.
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  • 113
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    An assessment of some preconditioning techniques in shell problems (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 897-906 
    Details
    ISSN: 1069-8299
    Keywords: preconditioning ; conjugate gradient ; finite elements ; shells ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Preconditioned Krylov subspace methods have proved to be efficient in solving large, sparse linear systems in many areas of scientific computing. The success of these methods in many cases is due to the existence of good preconditioning techniques. In problems of structural mechanics, like the analysis of heat transfer and deformation of solid bodies, iterative solution of the linear equation system can result in a significant reduction of computing time. Also many preconditioning techniques can be applied to these problems, thus facilitating the choice of an optimal preconditioning on the particular computer architecture available.However, in the analysis of thin shells the situation is not so transparent. It is well known that the stiffness matrices generated by the FE discretization of thin shells are very ill-conditioned. Thus, many preconditioning techniques fail to converge or they converge too slowly to be competitive with direct solvers. In this study, the performance of some general preconditioning techniques on shell problems is examined. © 1998 John Wiley & Sons, Ltd.
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  • 114
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    On the eigensystems of the Stokes operator discretized by the Q1-P0 finite element method (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 959-961 
    Details
    ISSN: 1069-8299
    Keywords: Stokes problem ; finite element ; eigensystems ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The use of mixed finite element methods in discretizing the Stokes equations leads to systems involving the so-called pressure matrix. Some new spectral properties of this important matrix are here presented for the Q1-P0 element. © 1998 John Wiley & Sons, Ltd.
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  • 115
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    Geometric non-linear analysis of space shell structures using generalized conforming flat shell elements - for space shell structures (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 941-957 
    Details
    ISSN: 1069-8299
    Keywords: geometrical non-linear ; UL formulation ; drilling degrees of freedom ; generalized conforming ; arc-length method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An updated Lagrangian formulation of the generalized conforming flat shell element with drilling degrees of freedom is derived based on the incremental equation of virtual work of a three-dimensional (3D) continuum for a purely geometric non-linear analysis of the space structure. While solving the non-linear equations, the Euler-Newton method and modified Euler-Newton method are used in static analyses, and the modified arc-length method and Newton arc-length method for post-buckling problems. A number of numerical examples are given to demonstrate the effectiveness of the proposed approach and programs. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 7 Ill.
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  • 116
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    Finite element analysis of cylindrical gears (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 963-975 
    Details
    ISSN: 1069-8299
    Keywords: cylindrical gears ; load distribution ; stress ; deformation ; stiffness ; FEM ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method, namely the normal stiffness matrix along contact line (NSMACL) method, for analysing gears is proposed. Three-dimensional (3D) finite element (FE) solid models have been established. Cylindrical gears - spur and helical, external and internal, hobbling and slotting, different parameters and materials - can be analysed using these models. Results such as load distribution along the contact lines, deformations and stiffness at any contact position, and contact stresses are presented. Calculation results show that the trend of gear tooth deformation coincides with the tested ones using the dynamic speckle photography method. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 11 Ill.
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  • 117
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    A quadratic assumed natural strain triangular element for plate bending analysis (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 1013-1025 
    Details
    ISSN: 1069-8299
    Keywords: assumed natural strain ; plate bending ; triangular ; finite element ; six-node ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, a six-node triangular C0 plate bending element is developed by the assumed natural strain method. In the element, all the sampled natural transverse shear strains are chosen such that the latter has a favourable constraint index and the strains are optimized with respect to a linear pure moment field. The element passes the patch tests, yields satisfactory accuracy and shows no sign of shear locking in all the problems considered. Copyright © 1998 John Wiley & Sons, Ltd.
    Additional Material: 7 Ill.
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  • 118
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    Lagrange multipliers and the primal-dual method in the non-linear static equilibrium of multibody systems (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 463-472 
    Details
    ISSN: 1069-8299
    Keywords: multibody systems ; non-linear analysis ; static equilibrium ; constrained optimization ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents four different approaches to the solution of the non-linear static-equilibrium problem in complex linkages, including rigid and elastic elements. The error function is based on the potential of the system, and includes rigid elements by means of non-linear constraints. To this end use is made of Lagrange multipliers, along with the primal-dual method, penalty functions and weighted stiffness, comparisons being made between them. A Newton-Raphson method is used in seeking function minima for equilibrium positions. This procedure is also directly applicable to the other linkage and multibody position problems. © 1998 John Wiley & Sons, Ltd.
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  • 119
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    Temporal acceleration techniques for viscoelastic flows (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 473-491 
    Details
    ISSN: 1069-8299
    Keywords: temporal acceleration ; viscoelastic ; recovery ; Taylor-Galerkin ; finite elements ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a finite element study based on a technique associated with time extrapolation to accelerate the convergence rate to the steady state for viscoelastic flows. The approach adopted is a local extrapolation method attributed to Neville. Temporal extrapolation is embedded within a time-marching Taylor-Galerkin/pressure-correction scheme as applied to the solution of model channel flow, 4:1 plane contraction flow and flow past a circular cylinder. In particular, consideration is given to obtaining steady-state solutions for an Oldroyd-B model. When extrapolation is performed for stress and velocity or pressure, then stress and velocity overshoot, which consequently leads to divergence. In contrast, a stable numerical scheme emerges when only the stress is extrapolated. © 1998 John Wiley & Sons, Ltd.
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  • 120
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    Direct evaluation of boundary stresses in the 3D BEM of elastostatics (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 505-517 
    Details
    ISSN: 1069-8299
    Keywords: hypersingular integral equation ; continuous elements ; stress analysis ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, a method for the evaluation of boundary stresses directly from the BEM solution of elastostatic problems using the static boundary integral equation is presented. The technique is valid for corners and edges as well as smooth points on the boundary, and involves defining a new interpolation function for continuous elements which incorporate certain continuity conditions arising from the hypersingular nature of the integrals involved. An integration technique based on the singularity subtraction method using series expansions is adopted for the hypersingular intergrals. Results are shown to be more accurate than those obtained with conventional techniques. © 1998 John Wiley & Sons, Ltd.
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  • 121
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    Prediction of bimaterial thermal cracking by the boundary element method (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 539-547 
    Details
    ISSN: 1069-8299
    Keywords: boundary-only element analysis ; thermal cracking ; crack trajectory ; singular elements ; traction formula ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A boundary element procedure is developed concerning the prediction of the quasistatic crack growth in uniformly heated bimaterials. This procedure assumes the existence of an initial small crack in one of the two phases, and further cracking progress from this point due to thermal loading. The resulting mixed boundary value problem is solved by applying an incremental boundary-only method in conjunction with the multidomain technique. Fracture characterizing parameters are evaluated utilizing special crack tip singular elements and appropriate formulas. The crack path is predicted using the strain energy release rate criterion, and the mesh is updated at the end of each increment. The presented results are in good agreement with previously reported experimental results and those obtained by the finite element method. Various numerical studies were conducted and interpreted concerning crack-path dependence on individual material property mismatch. © 1998 John Wiley & Sons, Ltd.
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  • 122
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    Finite element computations for the Reissner-Mindlin plate model (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 1119-1131 
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    ISSN: 1069-8299
    Keywords: Reissner-Mindlin plate ; finite element method ; p version ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We consider the finite element (FE) approximation of the Reissner-Mindlin (RM) plate model, and indicate how to design meshes that yield accurate results when the p/hp version of the standard FE method is used. These guidelines allow quantities of engineering interest to be predicted numerically with great confidence near the boundary. We illustrate this through numerical computations in the case when both boundary layers and corner singularities are present. Copyright © 1998 John Wiley & Sons, Ltd.
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  • 123
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    Static and free vibrational analysis of rectangular plates by the differential quadrature element method (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 1133-1141 
    Details
    ISSN: 1069-8299
    Keywords: differential quadrature element method ; rectangular plate ; static analysis ; free vibration analysis ; numerical method ; stepped plate ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The differential quadrature (DQ) element method proposed by Wang and Gu in 1997 has been extended to analyse rectangular plate problems. The methodology is worked out in detail and some numerical examples are given. Copyright © 1998 John Wiley & Sons, Ltd.
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  • 124
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    Formulation of a super-element for the dynamic problem of a cracked plate (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 1143-1154 
    Details
    ISSN: 1069-8299
    Keywords: super-element ; cracked plate ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: On the formulation of a super-element for the dynamic problem of a cracked plate, a geometric series of similar elements is designed. This group of elements is generated layer by layer, approaching infinitely small size around the point of singularity. The relations between similar elements for the stiffness matrix and the mass matrix are established. The concept of matrix condensation is applied to formulate the super-element by using these relationships. This method presents a feasible approach to the solution of the cracked problem with an arbitrary order of stress singularity. The method is computationally economical. Copyright © 1998 John Wiley & Sons, Ltd.
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  • 125
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    A linear θ method applied to 2D time-domain BEM (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 1171-1179 
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    ISSN: 1069-8299
    Keywords: linear θ method ; time-domain BEM ; stability ; scalar wave ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A linear θ method is used in this paper to improve the stability of the standard time-domain BEM formulation. The time-stepping procedure is similar to that of the Wilson θ method; however, unlike in the FEM, where linear time variation of acceleration (for elastodynamic problems) is assumed, here linear time variation for both potential and flux (for scalar waves) is assumed in the time interval θΔt. A comparison between numerical results obtained from the standard formulation and from the linear θ method studied here shows the latter to be more stable than the former. The effect of varying θ for different values of time steps is also studied in this paper. Copyright © 1998 John Wiley & Sons, Ltd.
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    Mixed-interpolated elements for thin shells (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 1155-1170 
    Details
    ISSN: 1069-8299
    Keywords: shell problem ; Naghdi model ; finite elements ; mixed elements ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The subject of this work is the construction of some special finite elements for the numerical solution of Naghdi cylindrical shell problems. The standard numerical approximation of the shell problem is subjected to the shear and membrane locking phenomenon, i.e. the numerical solution degenerates for low thickness. The most common way to avoid locking is the use of modified bilinear forms to describe the shear and membrane energy of the shell. In this paper we build a family of special finite elements that still follow the above strategy by introducing a linear operator that reduces the influence both of the shear and membrane energy terms. The main idea comes from the non-standard mixed interpolated tensorial components (MITC) formulation for Reissner-Mindlin plates. The performance of the new elements is then tested for solving benchmark problems involving very thin shells. The results show both the properties of convergence and robustness. Copyright © 1998 John Wiley & Sons, Ltd.
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    Harmonic projection methods for large non-symmetric eigenvalue problems (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 5 (1998), S. 33-55 
    Details
    ISSN: 1070-5325
    Keywords: eigenvalues ; Arnoldi ; Krylov subspaces ; preconditioning ; Davidson's method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The problem of finding interior eigenvalues of a large nonsymmetric matrix is examined. A procedure for extracting approximate eigenpairs from a subspace is discussed. It is related to the Rayleigh-Ritz procedure, but is designed for finding interior eigenvalues. Harmonic Ritz values and other approximate eigenvalues are generated. This procedure can be applied to the Arnoldi method, to preconditioning methods, and to other methods for nonsymmetric eigenvalue problems that use the Rayleigh-Ritz procedure. The subject of estimating the boundary of the entire spectrum is briefly discussed, and the importance of preconditioning for interior eigenvalue problems is mentioned. © 1998 John Wiley & Sons, Ltd.
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    Approximating minimum norm solutions of rank-deficient least squares problems (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 5 (1998), S. 79-99 
    Details
    ISSN: 1070-5325
    Keywords: bidiagonalization ; least squares ; minimum norm solution ; rank-deficient ; regularization ; Riley-Golub iteration ; singular value decomposition ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we consider the solution of linear least squares problems          minx∥Ax - b∥22 where the matrix A ∊ Rm × n is rank deficient. Put p = min{m, n}, let σi, i = 1, 2,…, p, denote the singular values of A, and let ui and vi denote the corresponding left and right singular vectors. Then the minimum norm solution of the least squares problem has the form x* = ∫ri = 1(uTib/σi)vi, where r ≤ p is the rank of A.The Riley-Golub iteration,          xk + 1 = arg minx{∥Ax - b∥22 + λ∥x - xk∥22} converges to the minimum norm solution if x0 is chosen equal to zero. The iteration is implemented so that it takes advantage of a bidiagonal decomposition of A. Thus modified, the iteration requires only O(p) flops (floating point operations). A further gain of using the bidiagonalization of A is that both the singular values σi and the scalar products uTib can be computed at marginal extra cost. Moreover, we determine the regularization parameter, λ, and the number of iterations, k, in a way that minimizes the difference x* - xk with respect to a certain norm. Explicit rules are derived for calculating these parameters.One advantage of our approach is that the numerical rank can be easily determined by using the singular values. Furthermore, by the iterative procedure, x* is approximated without computing the singular vectors of A. This gives a fast and reliable method for approximating minimum norm solutions of well-conditioned rank-deficient least squares problems. Numerical experiments illustrate the viability of our ideas, and demonstrate that the new method gives more accurate approximations than an approach based on a QR decomposition with column pivoting. © 1998 John Wiley & Sons, Ltd.
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    Convergence analysis of an iterative aggregation/disaggregation method for computing stationary probability vectors of stochastic matrices (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 5 (1998), S. 253-274 
    Details
    ISSN: 1070-5325
    Keywords: stochastic matrix ; aggregation/disaggregation iterative methods ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: An aggregation/disaggregation iterative algorithm for computing stationary probability vectors of stochastic matrices is analysed. Two convergence results are presented. First, it is shown that fast, global convergence can be achieved provided that a sufficiently high number of relaxations is performed on the fine level. Second, local convergence is shown to take place with just one relaxation performed on the fine level. The convergence proofs are general and require no assumptions on the magnitude of off-diagonal elements (blocks). Furthermore, a relationship between the errors on the fine and on the coarse level is described. To illustrate the theory, the results of some numerical experiments are presented. © 1998 John Wiley & Sons, Ltd.
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    Domain embedding preconditioners for mixed systems (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 5 (1998), S. 321-345 
    Details
    ISSN: 1070-5325
    Keywords: second order elliptic problems ; Dirichlet boundary conditions ; mixed finite elements ; preconditioning ; domain embedding ; auxiliary space method ; non-conforming finite elements ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we study block diagonal preconditioners for mixed systems derived from the Dirichlet problems for second order elliptic equations. The main purpose is to discuss how an embedding of the original computational domain into a simpler extended can be utilized in this case. We show that a family of uniform preconditioners for the corresponding problem on the extended, or fictitious, domain leads directly to uniform preconditioners for the original problem. This is in contrast to the situation for the standard finite element method, where the domain embedding approach for the Dirichlet problem is less obvious. Copyright © 1999 John Wiley & Sons, Ltd.
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    Operator trigonometry of the model problem (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 5 (1998), S. 377-399 
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    ISSN: 1070-5325
    Keywords: iterative methods ; operator trigonometry ; anti-eigenvector ; Dirichlet problem ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The new operator-trigonometric theory for iterative linear solvers is illustrated by working out its details for the classical model problem for numerical partial differential equations: the Dirichlet problem on the unit square. Copyright © 1999 John Wiley & Sons, Ltd.
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    Convergence results for 3D sparse grid approaches (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 5 (1998), S. 363-376 
    Details
    ISSN: 1070-5325
    Keywords: convergence ; multigrid ; sparse grids ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The convergence behaviour of solution algorithms is investigated for the anisotropic Poisson problem on partially ordered, sparse families of regular grids in 3D. In order to study multilevel techniques on sparse families of grids, first we consider the convergence of a two-level algorithm that applies semi-coarsening successively in each of the coordinate directions. This algorithm shows good convergence, but recursive application of the successive semi-coarsening is not sufficiently efficient. Therefore we introduce another algorithm, which uses collective 3D semi-coarsened coarse grid corrections. The convergence behaviour of this collective version is worse, due to the lack of correspondence between the solutions on the different grids. By solving for the trivial solution we demonstrate that a good convergence behaviour of the collective version of the algorithm can be retained when the different solutions are sufficiently coherent. In order to solve also non-trivial problems, we develop a defect correction process. This algorithm makes use of hierarchical smoothing in order to deal with the problems related to the lack of coherence between the solutions on the different grids. Now good convergence rates are obtained also for non-trivial solutions. All convergence results are obtained for two-level processes. The results show convergence rates which are bounded, independent of the discretisation level and of the anisotropy in the problem. Copyright © 1999 John Wiley & Sons, Ltd.
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    Preconditioned solution methods for large scale problems in scientific computations PRISM '97 (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 5 (1998), S. 319-319 
    Details
    ISSN: 1070-5325
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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    Parallel multilevel preconditioners for thin smooth shell finite element analysis (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 5 (1998), S. 401-440 
    Details
    ISSN: 1070-5325
    Keywords: thin shell problems ; linear partial differential equations ; parallel computing ; multilevel methods ; additive splittings ; finite element methods ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In recent years multilevel preconditioners like BPX have become more and more popular for solving second-order elliptic finite element discretizations by iterative methods. P. Oswald has adapted these methods for discretizations of the fourth order biharmonic problem by rectangular conforming Bogner-Fox-Schmit elements and non-conforming Adini elements and has derived optimal estimates for the condition numbers of the preconditioned linear systems. In this paper we generalize the results from Oswald to the construction of parallel BPX and multilevel diagonal scaling (MDS-BPX) preconditioners for the elasticity problem of thin smooth shells in connection with Koiter's shell theory. We use the two discretizations mentioned above and the preconditioned conjugate gradient method as iterative method. The parallelization concept is based on a non-overlapping domain decomposition data structure. We describe the implementations of the parallel multilevel preconditioners. Finally, we show numerical results for some shells representing elliptic, parabolic, hyperbolic and more complicated classes. In addition, the influence of the thickness parameter and the loading on the preconditioner are investigated experimentally. Copyright © 1999 John Wiley & Sons, Ltd.
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    Optimal v-cycle algebraic multilevel preconditioning (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 5 (1998), S. 441-459 
    Details
    ISSN: 1070-5325
    Keywords: iterative methods for linear systems ; acceleration of convergence ; preconditioning ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider algebraic multilevel preconditioning methods based on the recursive use of a 2 × 2 block incomplete factorization procedure in which the Schur complement is approximated by a coarse grid matrix. As is well known, for discrete second-order elliptic PDEs, optimal convergence properties are proved for such basic two-level schemes under mild assumptions on the PDE coefficients, but their recursive use in a simple V-cycle algorithm does not generally lead to optimal order convergence.In the present paper, we analyse the combination of these techniques with a smoothing procedure much the same as the one used in standard multigrid algorithms, except that smoothing is not required on the finest grid. Theoretical results prove optimal convergence properties for the V-cycle under an assumption similar to the ‘approximation property’ of the classical multigrid convergence theory. On the other hand, numerical experiments made on both 2D and 3D problems show that the condition number is close to that of the two-level method. Further, the method appears robust in the presence of discontinuity and anisotropy, even when the material interfaces are not aligned with the coarse grid. Copyright © 1999 John Wiley & Sons, Ltd.
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    Computing the nearest diagonally dominant matrix (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 5 (1998), S. 461-474 
    Details
    ISSN: 1070-5325
    Keywords: diagonally dominant matrices ; matrix cones ; Dykstra's algorithm ; Kuhn-Tucker conditions ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We solve the problem of minimizing the distance from a given matrix to the set of symmetric and diagonally dominant matrices. First, we characterize the projection onto the cone of diagonally dominant matrices with positive diagonal, and then we apply Dykstra's alternating projection algorithm on this cone and on the subspace of symmetric matrices to obtain the solution. We discuss implementation details and present encouraging preliminary numerical results. Copyright © 1999 John Wiley & Sons, Ltd.
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    Efficient computation of sparse approximate inverses (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 5 (1998), S. 57-71 
    Details
    ISSN: 1070-5325
    Keywords: preconditioning ; sparse approximate inverse ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We investigate different methods for computing a sparse approximate inverse M for a given sparse matrix A by minimizing ∥AM - E∥ in the Frobenius norm. Such methods are very useful for deriving preconditioners in iterative solvers, especially in a parallel environment. We compare different strategies for choosing the sparsity structure of M and different ways for solving the small least squares problem that are related to the computation of each column of M. Especially we show how we can take full advantage of the sparsity of A. © 1998 John Wiley & Sons, Ltd.
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    On M-multisplittings of singular M-matrices with application to Markov chains (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 5 (1998), S. 299-311 
    Details
    ISSN: 1070-5325
    Keywords: iterative methods ; singular linear systems ; index of a matrix ; M-splittings ; multi-splittings ; Q-matrices ; Markov chains ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Given a singular M-matrix of a linear system, convergent conditions under which iterative schemes based on M-multisplittings are studied. Two of those conditions, the index of the iteration matrix and its spectral radius are investigated and related to those of the M-matrix. Furthermore, a parallel multisplitting iteration scheme for solving singular linear systems is suggested which can be applied to practical problems such as Poisson and elasticity problems under certain boundary conditions, the Neumann problem, and in Markov chains. A discussion of that multisplitting scheme, based on Gauss-Seidel type splittings is given for computing the stationary distribution vector of Markov chains. In this case a computational viable algorithm can be constructed, since only the nonsingularity of one weighting matrix of the multisplitting is needed. © 1998 John Wiley & Sons, Ltd.
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    A new adaptive GMRES algorithm for achieving high accuracy (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 5 (1998), S. 275-297 
    Details
    ISSN: 1070-5325
    Keywords: GMRES method ; Krylov subspace methods ; non-symmetric linear systems ; homotopy curve tracking ; sparse matrix ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: GMRES(k) is widely used for solving non-symmetric linear systems. However, it is inadequate either when it converges only for k close to the problem size or when numerical error in the modified Gram-Schmidt process used in the GMRES orthogonalization phase dramatically affects the algorithm performance. An adaptive version of GMRES(k) which tunes the restart value k based on criteria estimating the GMRES convergence rate for the given problem is proposed here. This adaptive GMRES(k) procedure outperforms standard GMRES(k), several other GMRES-like methods, and QMR on actual large scale sparse structural mechanics postbuckling and analog circuit simulation problems. There are some applications, such as homotopy methods for high Reynolds number viscous flows, solid mechanics postbuckling analysis, and analog circuit simulation, where very high accuracy in the linear system solutions is essential. In this context, the modified Gram-Schmidt process in GMRES, can fail causing the entire GMRES iteration to fail. It is shown that the adaptive GMRES(k) with the orthogonalization performed by Householder transformations succeeds whenever GMRES(k) with the orthogonalization performed by the modified Gram-Schmidt process fails, and the extra cost of computing Householder transformations is justified for these applications. © 1998 John Wiley & Sons, Ltd.
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    Semi-coarsening AMLI algorithms for elasticity problems (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 5 (1998), S. 347-362 
    Details
    ISSN: 1070-5325
    Keywords: almost incompressible elasticity ; finite elements ; semi-coarsening refinement ; algebraic multilevel ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The constant γ in the strengthened Cauchy-Buniakowski-Schwarc (CBS) inequality plays a key role in the convergence analysis of the multilevel iterative methods. We consider in this paper the approximation of the two-dimensional elasticity problem by bilinear rectangle finite elements. Two semi-coarsening refinement procedures are studied. We prove for both cases new estimates of the constant γ, uniformly on the Poisson ratio.As a result of the presented analysis we obtain an optimal order algebraic multiLevel iteration (AMLI) method for the case of balanced semi-coarsening mesh refinement. The total computational complexity of the algorithm is proportional to the size of the discrete problem with a proportionality constant independent of the Poisson ratio, that is, the algorithm is of optimal order for almost incompressible elasticity problems. Copyright © 1999 John Wiley & Sons, Ltd.
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    An automatic mesh coarsening technique for Delaunay triangulations (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 59-63 
    Details
    ISSN: 1069-8299
    Keywords: Delaunay triangulation ; mesh colouring ; mesh coarsening ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new algorithm is described for automatic coarsening of Delaunay triangulations. The method automatically identifies the nodes of the mesh which are candidates for deletion in each region to be coarsened. The mesh coarsening procedure is to regenerate a Delaunay triangulation for all the remaining nodes in the solution domain. The adapted mesh retains a high quality for two reasons: (i) because a set of nodes have been used to obtain the coarse mesh, which are equidistant apart in some sense defined by the original mesh; (ii) because the triangulation is Delaunay. A two-dimensional example demonstrates the quality of the mesh after coarsening. © 1998 John Wiley & Sons, Ltd.
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    Derivation of a rectangular finite element for potential problems from consistency criteria (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 35-42 
    Details
    ISSN: 1069-8299
    Keywords: potential problems ; rectangular finite element ; consistency criteria ; rigid body modes ; constant straining modes ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This short paper demonstrates how the matrix for a 4-node potential finite element can be derived from the conditions of ‘rigid body movement’, symmetry and consistency, and the requirement that the element solve exactly the case of φ=xy. This derivation is intended to be a simple illustration of the ideas of Bergan and others. © 1998 John Wiley & Sons, Ltd.
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    A finite element analysis of multiphase immiscible flow in deforming porous media for subsurface systems (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 135-149 
    Details
    ISSN: 1069-8299
    Keywords: multiphase immiscible flow ; deforming porous media ; fully coupled ; soil displacements ; fluid pressures ; finite element method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A fully coupled numerical model has been developed which describes multiphase fluid flow through soil: namely gas, water and a non-aqueous phase liquid (NAPL) in a deforming porous media for subsurface systems. A multiphase flow model, based on the two-phase flow model of Brooks and Corey, is presented to express the dependence of saturation and relative permeability on the capillary pressure. Non-linear saturation and relative permeability functions are incorporated into a Galerkin finite element model which is subsequently used to simulate multiphase immiscible fluid flow under saturated and unsaturated conditions in porous media. The governing partial differential equations, in terms of soil displacements and fluid pressures, which are coupled and non-linear, are solved by the finite element method. Numerical implementation of the formulation is discussed, and example problems demonstrate the model and solution procedure. © 1998 John Wiley & Sons, Ltd.
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    The use of evolutionary-genetic analogy in numerical analysis (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 151-160 
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    ISSN: 1069-8299
    Keywords: genetic algorithms ; evolutionary-genetic analogy ; heat transfer ; finite elements ; numerical analysis ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new approach was developed for the analysis of problems of physics governed by laws of conservation. The methodology establishes an analogy between various aspects of evolution and genetics of life processes and inanimate physical systems. This analogy is then used to generate solutions to physical problems in a similar way to which organisms in nature solve problems imposed by environmental constraints. Finite difference and finite elements approximations are used in the numerical implementation of the method and a simple two-dimensional problem is solved to illustrate the method. © 1998 John Wiley & Sons, Ltd.
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    Numerical visualization of oscillatory flow around a circular cylinder at Re=200 and KC=20 - an aperiodic flow case (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 181-194 
    Details
    ISSN: 1069-8299
    Keywords: oscillating flow ; Keulegan-Carpenter number ; finite element method ; in-line force ; transverse force ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The results of a numerical study of the viscous oscillating flow around a circular cylinder at Reynolds number=200 and Keulegan-Carpenter number=20 are presented. The finite element method was used for the solution of the Navier-Stokes equations, in the formulation where the streamfunction and the vorticity are the field variables. The computation revealed a complicated flow pattern at which the flow is not periodic but switches between different modes at various oscillation cycles. The vortex shedding patterns occurring at different cycles were identified by means of numerical flow visualization. The traces of the hydrodynamic forces were derived from the solution, and the hydrodynamic coefficients of the in-line force were evaluated. © 1998 John Wiley & Sons, Ltd.
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    Boundary spectral strip for geometries with arbitrary curvature (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 219-228 
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    ISSN: 1069-8299
    Keywords: boundary integral ; spectral strip ; curvature geometries ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The non-element boundary spectral strip method is developed for solution of problems in curvature domains. The method, which uses a spectral Fourier approximation for expansion of the variables along the boundaries, shows an exponential convergence behaviour. A remarkable reduction in problem size and improved accuracy of results is achieved by the method as compared to the boundary element method. The method is illustrated by some physical problems from elastostatics. © 1998 John Wiley & Sons, Ltd.
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    Simulation of surface tension effect during filling of a thin section cavity via an interface element (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 229-240 
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    ISSN: 1069-8299
    Keywords: filling of thin section ; finite element method ; surface tension ; interface element ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An interface element to model the pressure discontinuity due to surface tension when applied to the filling of a thin section cavity is presented. The equations used to form the element matrix for the interface element are the line integral form of the continuity and momentum equations. During the development of the finite element model, the pressure difference across the free surface due to surface tension is treated as an additional traction and is applied to all element sides which form the free surface. Simple numerical examples are then presented to illustrate the technique on the filling of a rectangular thin section cavity. © 1998 John Wiley & Sons, Ltd.
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    Classical numerical methods in engineering: a note on existential quantifier elimination under parametric inequality constraints (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 103-134 
    Details
    ISSN: 1069-8299
    Keywords: computational quantifier elimination ; edge crack ; feasibility (consistency) conditions ; fracture mechanics ; numerical methods in engineering ; parametric inequality constraints ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, an attempt is made to show the usefulness of computational quantifier elimination (CQE) techniques in computer algebra inside classical numerical methods in engineering for the derivation of feasibility (consistency) conditions in problems with weakly parametric linear inequality constraints (with the parameters appearing only in their right-hand sides). A simple, but non-trivial, straight edge-crack problem in fracture mechanics under linear inequality constraints both on the applied loading along the crack faces and on the value of the stress intensity factor at the crack tip (associated with the Green/weight function method, numerical approximations and classical numerical integration) is used for an elementary illustration of the proposed approach. In this application, the method used tries to imitate the theoretical principle of the linear programming methods. The manually obtained related result is expressed as a disjunction of conjunctions of inequalities (as is frequently the case in similar CQE problems), and concrete numerical results are also displayed. The related influence of various approximations and the application of the trapezoidal quadrature rule are also considered in some detail. Further possibilities could concern the application of the approach to other numerical methods in engineering (such as to the finite and the boundary element methods, to singular and hypersingular integral equation methods, etc.) combined with efficient algorithms for linear inequality constraints such as the old Fourier and the recent Weispfenning elimination methods. © 1998 John Wiley & Sons, Ltd.
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    Two-dimensional mesh redistribution and solution of singular boundary value problems (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 797-808 
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    ISSN: 1069-8299
    Keywords: mesh equidistribution ; area preserving map ; singular BVP ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, an adaptive mesh method is employed to solve a class of singular boundary value problems. The approach is based on an area-preserving map and some mesh shape control in two-dimensional space. Two benchmark problems, which both involve singularities in physical domains, are tested. © 1998 John Wiley & Sons, Ltd.
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    A note on the class of weakly coupled problems of non-stationary piezoelectricity (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 839-847 
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    ISSN: 1069-8299
    Keywords: coupled models of dynamic electroelasticity ; generalized solutions ; metrics weaker than L2 ; spectrum of a priori estimates ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper we deal with a model of coupled non-stationary electroelasticity with displacements and potential given on the boundary of a body. We construct a numerical scheme for modelling electromechanical interactions in the body, and present a spectrum of a priori estimates for the solution of this scheme. Such estimates allow us to prove the convergence of the scheme to a generalized solution of the differential problem from W22(QT) with the second order of accuracy in a weaker than L2 metric. © 1998 John Wiley & Sons, Ltd.
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    A parallel diagonally iterated RK method for convection-diffusion and stiff problems (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 821-837 
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    ISSN: 1069-8299
    Keywords: diagonally implicit Runge-Kutta methods ; parallelism ; stiffness ; stability ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper we propose a parallel diagonal iteration process for solving a low-order implicit Runge-Kutta method of Lagrange type. The resulting scheme can be regarded as a parallel singly diagonally implicit Runge-Kutta (PSDIRK) method and it is strongly A-stable when the classical linear test model is used. On a two-processor computer, this method requires the solution of two implicit relations (sequential time units) per step and per processor. We compare our method with some sequential and parallel methods from the literature for solving linear as well as non-linear stiff problems and semidiscretized convection-diffusion equations. The numerical experiments show the behaviour of our method with regard to the other methods. © 1998 John Wiley & Sons, Ltd.
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    A note on finding nearest neighbours and constructing Delaunay triangulation in the plane (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 871-877 
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    ISSN: 1069-8299
    Keywords: nearest neighbours ; Voronoi diagram ; Delaunay triangulation ; computational geometry ; algorithms ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper deals with the largest interior angle property of the Voronoi nearest neighbours and the Delaunay triangulation in two dimensions. It is indicated that each interior angle opposite to an edge of a Delaunay triangle is the largest of the interior angles opposite the same edge of all possible triangles on the same side. Based on this property, the algorithms for finding the Voronoi neighbours of a point (site) and for constructing the Delaunay triangulation are presented. The algorithms are especially useful for the meshless methods developed in recent years. © 1998 John Wiley & Sons, Ltd.
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    Numerical simulation of as-quenched hardness in a steel specimen of complex form (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 277-285 
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    ISSN: 1069-8299
    Keywords: numerical simulation ; steel ; quenching ; finite volume method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: On the basis of the control volume method the algorithm and computer program for prediction of the hardness distribution in quenched steel specimens with complex geometries have been developed. The algorithm and computer program are designed to solve 2D situation problems such as the quenching of complex cylinders, cones, spheres, etc. The computer program consists of three parts: automatic computation of domain and grid generation, computation of cooling curve in grid-points, and computation of hardness in grid-points. The mathematical model has been tested experimentally. The test showed that the model describes the hardness distribution in a quenched steel specimen of a complex form, with quite satisfactory accuracy. © 1998 John Wiley & Sons, Ltd.
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    On two equivalent thin plate finite elements (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 271-275 
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    ISSN: 1069-8299
    Keywords: basis transformation ; interpolations ; finite elements ; thin plates ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The 9 df thin plate element of Mohr and Mohr uses cubic interpolation to obtain values of w at the third points of the element sides, in turn interpolating from these and the vertex values within the element. Recently this element has been modified and successfully applied to ‘potential’ problems. Subsequently it was found that the interpolations of the element of Bazeley et al. (1965, 1968) gave identical results for potential problems. In the present paper it is shown that this is because the interpolations of the two elements are exactly equivalent. © 1998 John Wiley & Sons, Ltd.
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    A way to split the Navier-Stokes equations in the context of the vortex method (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 313-319 
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    ISSN: 1069-8299
    Keywords: fluid mechanics ; vortex dynamics ; viscous flow ; Navier-Stokes equation ; vortex methods ; splitting procedure ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical scheme has been obtained rigorously from the initial-boundary value problem for the Navier-Stokes (NS) equations in the context of the vortex method. The technique is based on a transformation of the NS equation into a parabolic equation which has an exact solution. The numerical scheme is derived by expanding the exact solution in Taylor series in powers of a small time interval. Numerical implementation is developed with use of vortex particles to represent the vortex flow domain. The method is used to solve practical engineering problems. The technique can also incorporate turbulence modelling. © 1998 John Wiley & Sons, Ltd.
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    Finite element integral equation modelling of a thin wire loop antenna (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 347-354 
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    ISSN: 1069-8299
    Keywords: thin wire loop antenna ; integro-differential equation ; frequency domain ; current distribution ; the weak formulation ; finite element technique ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The circular loop antenna is analysed by using the electric field integro-differential equation in the frequency domain. The weak form of the integro-differential is derived and then the current distribution along the circular loop antenna is calculated by solving the resulting equation via the finite element technique. Accurate results are obtained using the linear shape and test functions. © 1998 John Wiley & Sons, Ltd.
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    A boundary element method for modelling cracks along material interfaces in transient dynamics (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 355-365 
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    ISSN: 1069-8299
    Keywords: transient dynamics ; interaction of the crack sides ; crack propagation ; time domain formulation ; boundary element method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: For two-dimensional solids the multiregion concept and the time-domain approach in the boundary element method are employed to model cracks in transient dynamics. The propagation of cracks and the closing and opening of crack sides are simulated by disconnecting and connecting degrees of freedom of a stationary mesh, as was also demonstrated recently in statics by Beer. An iterative technique is developed to determine the changes of the extent of the area where there is connection, contact or no contact at the interface between dynamically loaded regions. © 1998 John Wiley & Sons, Ltd.
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    A finite element solution procedure for porous medium with fluid flow and electromechanical coupling (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 381-392 
    Details
    ISSN: 1069-8299
    Keywords: porous medium ; fluid flow ; electromechanical coupling ; FEM ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We consider a coupled problem of the deformation of a porous solid, flow of a compressible fluid and the electrical field in the mixture. The governing equations consist of balance of the linear momentum of solid and of fluid, continuity equations of the fluid and current density, and a generalized form of Darcy's law which includes electrokinetic coupling. The compressibility of the solid and the fluid are taken into account. We transform these equations to the corresponding finite element relations by employing the principle of virtual work and the Galerkin procedure. The nodal point variables in our general formulation are displacements of solid, fluid pore pressure, relative velocity of the fluid and electrical potential. Derivation of the FE equations is presented for small displacements and elastic solid, which can further be generalized to large displacements and inelastic behaviour of the solid skeleton.According to this formulation we can include general boundary conditions for the solid, relative velocity of the fluid, fluid pressure, current density and electrical potential. The dynamic-type non-symmetric system of equations is solved through the Newmark procedure, while in the case of neglect of inertial terms we use the Euler method.Numerical examples, solved by our general-purpose FE package PAK, are taken from biomechanics. The results are compared with those available in the literature, demonstrating the correctness and generality of the procedure presented. © 1998 John Wiley & Sons, Ltd.
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    3D adaptive mesh refinement (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 397-407 
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    ISSN: 1069-8299
    Keywords: 3D mesh generation ; adaptive refinement ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An adaptive finite element (FE) method for the solution of three-dimensional elasto-static problems is described. The computational domain is represented by an assembly of tetrahedral elements and the mesh adaptation is achieved by a 3D bisection method using an error estimator procedure coupled with an automatic 3D mesh generator. The performance of the method is demonstrated using a number of examples. © 1998 John Wiley & Sons, Ltd.
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    The influence of plate size with double cracks on stress intensity factor (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 429-436 
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    ISSN: 1069-8299
    Keywords: stress intensity factor (SIF) ; singular finite element ; double cracks ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Using the quasi-compatible finite element method advanced by Zhichao and Lisu (1990), the influence of the size of a plate with double cracks on the stress intensity factor is studied. Many numerical computations are carried out and various data, curves and formulae are given. It is shown clearly how the stress intensity factors of double cracks are affected by the size of the cracked body. © 1998 John Wiley & Sons, Ltd.
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    Highly efficient and accurate buffeting analysis of complex structures (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 559-567 
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    ISSN: 1069-8299
    Keywords: gust ; buffet ; random ; vibration ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A convenient and effective finite-element-based method for buffeting analysis of complex structures is presented. This method is very efficient for structures with the natural frequencies closely spaced because their corresponding modes and the cross-correlation terms between them should be included in the mode-superposition analysis. The imperfect correlation between gust excitations can also be dealt with conveniently. A numerical example is given which shows that by using this method the buffeting analysis of complex structures with thousands of degrees of freedom, dozens of imperfectly related excitations and a number of participating modes can be executed quite easily on an ordinary IBM/486 (or 586) personal computer. © 1998 John Wiley & Sons, Ltd.
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    A modified shell element method for determining 3D large strain distributions in sheet metal stampings (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 519-527 
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    ISSN: 1069-8299
    Keywords: shell element ; large strain ; sheet metal stamping ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a general method of large strain determination over the deformed surface of a sheet metal stamping. It is demonstrated that the conventional degenerated shell element with two normal rotation degrees of freedom is not suitable for large deformation, especially when large element rotation is present. This inaccuracy is primarily caused by the fact that the displacement field description used in the degenerated shell element is only a first-order approximation with respect to the two rotation degrees of freedom, and is therefore suitable only for small rotation angles. The new method presented in this paper replaces the two rotation DOFs with three new degrees of freedom to describe the rotation of the surface normal so that the element deformation can be accurately described with no limitation on the amount of deformation and rotation involved. The advantages of this new method are: (i) a linear and accurate expression of the displacement field in terms of nodal DOFs is obtained; (ii) the formulation is easily incorporated into any existing degenerated shell elements; (iii) the strain calculation is accurate for any amount of element rigid body rotation; (iv) if the method is used in surface grid analysis, the algorithm will not only provide correct surface strains, but also their variation through the thickness direction, i.e. the bending deformation. © 1998 John Wiley & Sons, Ltd.
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    Constructing the shape of a rod from eigenvalues (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 597-608 
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    ISSN: 1069-8299
    Keywords: inverse problems ; dual systems ; vibrating rod ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The discretization of the differential equation governing the axial vibration of a rod with varying cross-section leads to a specially structured matrix pencil. This paper deals with the reconstruction of this pencil from its spectrum. An iterative algorithm for this problem and an analytic characterization of complementary solutions are given. The method is demonstrated on some examples. © 1998 John Wiley & Sons, Ltd.
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    An adaptive finite element procedure for the image segmentation problem (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 621-632 
    Details
    ISSN: 1069-8299
    Keywords: segmentation ; finite elements ; adaptive ; image ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The image segmentation problem in computer vision is considered. Given a two-dimensional domain D and a function defined on it (the original image), the problem is to obtain a ‘cartoon’ associated with this function, namely to find a set of inner boundaries which divide D into subdomains (objects) in an optimal way. The optimality criterion used here is given by the Mumford-Shah (MS) and Blake-Zisserman model, which leads to a strongly non-linear problem. Related problems appear in multiphase continuum mechanics. An iterative procedure based on an h-adaptive finite element method is proposed for the solution of this problem. The mesh adaptivity enables an efficient solution technique, with the use of basic coarse discretization and a few local regions of high resolution where needed. © 1998 John Wiley & Sons, Ltd.
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    Error estimation in adaptive BEM by postprocessing interpolation (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 633-645 
    Details
    ISSN: 1069-8299
    Keywords: error estimation ; boundary elements ; adaptive mesh ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A posteriori error estimation for the boundary element method is developed. The nodal error is estimated from the difference of two solutions - one from the original BEM solution, and the other from interpolation of the original solution. Based on nodal errors, a matrix analysis is carried out to calculate the corresponding errors at source points. Two formulae for estimating global percentage errors are proposed in the paper. The first formula uses nodal errors directly to estimate element error, and the second uses an integral form to calculate element error to eliminate extremely high mesh concentration near areas with singular solutions. An h-version adaptive mesh refinement is implemented to study the accuracy of the proposed error estimation. Numerical examples show that the error estimator can correctly guide mesh refinement, and a final mesh can be obtained in a few iterations. © 1998 John Wiley & Sons, Ltd.
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    Accuracy and stability of semi-implicit finite difference advection schemes (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 647-655 
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    ISSN: 1069-8299
    Keywords: finite difference methods ; stability and convergence of numerical methods ; advection schemes ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper discusses implementation strategies for second-order finite difference discretizations of advection. Purely explicit and implicit methods both have disadvantages, and we consider semi-implicit schemes in which the flux is split into a primary implicit part and a secondary explicit correction. One-dimensional scalar advection is used as a model problem to analyse the leading order error terms and the stability of the schemes. Some of the splittings turn out to be unconditionally stable, but accuracy or monotonicity may deteriorate for large time steps. © 1998 John Wiley & Sons, Ltd.
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    A study of the backward-facing step problem using a generalized streamline formulation (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 697-708 
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    ISSN: 1069-8299
    Keywords: incompressible flow ; generalized streamline operator ; upwinding tensor ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the present work the backward-facing step problem is analysed in the framework of the finite element method. It is a very well-known benchmark problem for the numerical resolution of the incompressible Navier-Stokes equations. In particular, a generalized streamline operator technique (GSO) is used in the numerical approach to these equations. The results show very good agreement with those reported by other authors using different methodologies. © 1998 John Wiley & Sons, Ltd.
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    A conservative semi-Lagrangian algorithm for one-dimensional advection-diffusion (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 671-679 
    Details
    ISSN: 1069-8299
    Keywords: advection-diffusion ; semi-Lagrangian ; stability ; accuracy ; QUICKEST ; DISCUS ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes the incorporation of diffusive transport into the original semi-Lagrangian DISCUS algorithm for pure advection. An explicit treatment of diffusion is adopted following the approach used in the QUICKEST algorithm for advection-diffusion. The semi-Lagrangian treatment of the advection term relaxes the small time step restriction normally associated with Eulerian treatments of advection, but the Eulerian treatment of the diffusion term imposes conventional limitations on the scheme. Numerical experiments of advection-diffusion, however, indicate that DISCUS has advantages over the QUICKEST scheme for advection-diffusion in three key areas: stability, accuracy and computational efficiency. © 1998 John Wiley & Sons, Ltd.
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    Lattice-gas simulations of two-phase flow in porous media (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 709-717 
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    ISSN: 1069-8299
    Keywords: fluid dynamics ; multiphase-flow ; lattice gases ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Nearly all CFD methods can be considered as discretization methods for partial differential equations, such as finite difference, finite volume, finite element, spectral or boundary integral element methods. Virtually unrecognized by the scientific mainstream in computational fluid dynamics (CFD) during the last decade, a completely different approach to flow simulation has been developed in computational physics.The basic idea of lattice-gas solvers (LGS) goes back to the cellular automation concept of John von Neumann. LGS use objects (‘cells’), being extremely simple compared to finite boxes or finite elements. The state of a cell is usually described by only a few bits therefore often two orders of magnitude more cells are used for a simulation with LGS than ‘elements’ in a finite element computation. LGS are explicit time-stepping procedures; no equation systems have to be solved. Thus every time-step is extremely cheap in terms of CPU power compared to standard procedures, yet again much shorter time-steps have to be used. LGS are inherently parallel and are suitable to coarse-grain as well as to fine-grain parallelization.The paper will discuss some advantages and disadvantages of lattice-gas solvers and present LG simulation results of two-phase flow with moving boundaries on a microscope scale for a two-dimensional test geometry of randomly distributed equally sized disks where the effect of surface tension on the steady-state saturation will be demonstrated. © 1998 John Wiley & Sons, Ltd.
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    A weighted element patch based superconvergent stress extraction strategy (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 731-749 
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    ISSN: 1069-8299
    Keywords: superconvergence ; corrected conjoint polynomial ; weight functions ; element patch ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A superconvergent element patch based stress extraction strategy is proposed for general FE postprocessing and/or error estimation procedures in adaptive finite element analysis. Generalized weight functions are proposed for discrete least-square functionals, and a corrected conjoint polynomial fitting procedure is presented to ensure accurate stress extraction from the element domain once the primary level stress parameters have been evaluated. A numerical example is presented to fix the parameters of the weight functions. Several plane stress examples are solved using QUAD4 elements, and results are compared to those of the node patch based extraction method using the conventional conjoint polynomial method. It is shown that the proposed technique yields more accurate results with enhanced local convergence. Although the method may be applied to higher-order elements too, only QUAD4 elements are chosen for the present examples since the present secondary refitting strategy assumes superconvergent points only to be at element centroids. © 1998 John Wiley & Sons, Ltd.
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    Analysis of matrix-dependent multigrid algorithms (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 5 (1998), S. 165-202 
    Details
    ISSN: 1070-5325
    Keywords: diffusion problem ; discontinuous coefficients ; indefinite Helmholtz equation ; multigrid method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Convergence theory for a multigrid method with matrix-dependent restriction, prolongation and coarse-grid operators is developed for a class of SPD problems. It motivates the construction of improved multigrid versions for diffusion problems with discontinuous coefficients. A computational two-level analysis method for a class of separable problems is also available. It motivates the design of matrix-dependent multigrid algorithms and, in particular, multiple coarse-grid correction algorithms for highly indefinite equations. Numerical experiments show the advantage of the present methods for several examples. © 1998 John Wiley & Sons, Ltd.
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    Indefinitely preconditioned inexact Newton method for large sparse equality constrained non-linear programming problems (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 5 (1998), S. 219-247 
    Details
    ISSN: 1070-5325
    Keywords: non-linear programming ; sparse problems ; equality constraints ; inexact Newton method ; augmented Lagrangian function ; indefinite systems ; indefinite preconditioners ; conjugate gradient method ; residual smoothing ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: An inexact Newton algorithm for large sparse equality constrained non-linear programming problems is proposed. This algorithm is based on an indefinitely preconditioned smoothed conjugate gradient method applied to the linear KKT system and uses a simple augmented Lagrangian merit function for Armijo type stepsize selection. Most attention is devoted to the termination of the CG method, guaranteeing sufficient descent in every iteration and decreasing the number of required CG iterations, and especially, to the choice of a suitable preconditioner. We investigate four preconditioners, which have 2 × 2 block structure, and prove theoretically their good properties. The efficiency of the inexact Newton algorithm, together with a comparison of various preconditioners and strategies, is demonstrated by using a large collection of test problems. © 1998 John Wiley & Sons, Ltd.
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    The nearest ‘doubly stochastic’ matrix to a real matrix with the same first moment (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 5 (1998), S. 475-482 
    Details
    ISSN: 1070-5325
    Keywords: nearest doubly stochastic matrix ; alternating projections ; first moment ; normal cone ; RC1 ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Let T be an arbitrary n × n matrix with real entries. We consider the set of all matrices with a given complex number as an eigenvalue, as well as being given the corresponding left and right eigenvectors. We find the closest matrix A, in Frobenius norm, in this set to the matrix T. The normal cone to a matrix in this set is also obtained. We then investigate the problem of determining the closest ‘doubly stochastic’ (i.e., Ae = e and eT A = eT, but not necessarily non-negative) matrix A to T, subject to the constraints ${\bf e}_{1}^{\rm T} A^{k} {\bf e}_{1} = {\bf e}_{1}^{\rm T}T^{k}{\bf e}_{1}$, for k = 1, 2, … A complete solution is obtained via alternating projections on convex sets for the case k = 1, including when the matrix is non-negative. Copyright © 1999 John Wiley & Sons, Ltd.
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    A parallel multisplitting solution of the least squares problem (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 5 (1998), S. 11-31 
    Details
    ISSN: 1070-5325
    Keywords: least squares ; QR factorization ; iterative solvers ; parallel algorithms ; multisplitting ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The linear least squares problem, minx∥Ax - b∥2, is solved by applying a multisplitting (MS) strategy in which the system matrix is decomposed by columns into p blocks. The b and x vectors are partitioned consistently with the matrix decomposition. The global least squares problem is then replaced by a sequence of local least squares problems which can be solved in parallel by MS. In MS the solutions to the local problems are recombined using weighting matrices to pick out the appropriate components of each subproblem solution. A new two-stage algorithm which optimizes the global update each iteration is also given. For this algorithm the updates are obtained by finding the optimal update with respect to the weights of the recombination. For the least squares problem presented, the global update optimization can also be formulated as a least squares problem of dimension p. Theoretical results are presented which prove the convergence of the iterations. Numerical results which detail the iteration behavior relative to subproblem size, convergence criteria and recombination techniques are given. The two-stage MS strategy is shown to be effective for near-separable problems. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 5 Ill.
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    On the performance of various adaptive preconditioned GMRES strategies (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 5 (1998), S. 101-121 
    Details
    ISSN: 1070-5325
    Keywords: GMRES ; preconditioning ; invariant subspace ; deflation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper compares the performance on linear systems of equations of three similar adaptive accelerating strategies for restarted GMRES. The underlying idea is to adaptively use spectral information gathered from the Arnoldi process. The first strategy retains approximations to some eigenvectors from the previous restart and adds them to the Krylov subspace. The second strategy also uses approximated eigenvectors to define a preconditioner at each restart. This paper designs a third new strategy which combines elements of both previous approaches. Numerical results show that this new method is both more efficient and more robust. © 1998 John Wiley & Sons, Ltd.
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    On parallel solution of linear elasticity problems: Part I: theory (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 5 (1998), S. 123-139 
    Details
    ISSN: 1070-5325
    Keywords: elasticity problem ; separate displacement component ; preconditioned conjugate gradient method ; parallel algorithm ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The discretized linear elasticity problem is solved by the preconditioned conjugate gradient (pcg) method. Mainly we consider the linear isotropic case but we also comment on the more general linear orthotropic problem. The preconditioner is based on the separate displacement component (sdc) part of the equations of elasticity. The preconditioning system consists of two or three subsystems (in two or three dimensions) also called inner systems, each of which is solved by the incomplete factorization pcg-method, i.e., we perform inner iterations. A finite element discretization and node numbering giving a high degree of partial parallelism with equal processor load for the solution of these systems by the MIC(0) pcg method is presented. In general, the incomplete factorization requires an M-matrix. This property is studied for the elasticity problem. The rate of convergence of the pcg-method is analysed for different preconditionings based on the sdc-part of the elasticity equations. In the following two parts of this trilogy we will focus more on parallelism and implementation aspects. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 6 Ill.
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    Estimating a largest eigenvector by Lanczos and polynomial algorithms with a random start (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 5 (1998), S. 147-164 
    Details
    ISSN: 1070-5325
    Keywords: eigenvalue problem ; Lanczos method ; power method ; Krylov information ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study Lanczos and polynomial algorithms with random start for estimating an eigenvector corresponding to the largest eigenvalue of an n × n large symmetric positive definite matrix. We analyze the two error criteria: the randomized error and the randomized residual error. For the randomized error, we prove that it is not possible to get distribution-free bounds, i.e., the bounds must depend on the distribution of eigenvalues of the matrix. We supply such bounds and show that they depend on the ratio of the two largest eigenvalues. For the randomized residual error, distribution-free bounds exist and are provided in the paper. We also provide asymptotic bounds, as well as bounds depending on the ratio of the two largest eigenvalues. The bounds for the Lanczos algorithm may be helpful in a practical implementation and termination of this algorithm. © 1998 John Wiley & Sons, Ltd.
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    The structure of the boundary element matrix for the three-dimensional Dirichlet problem in elasticity (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 5 (1998), S. 203-217 
    Details
    ISSN: 1070-5325
    Keywords: boundary value problem ; boundary element method ; preconditioning ; fast Fourier transform ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The algebraic properties of the matrix arising for the three-dimensional Dirichlet problem for Lamé equations in a rotational domain by the boundary element method are considered. The use of the special basis leads to a matrix having a block structure with sparse blocks. The possible strategies for the efficient solution of the above problem are discussed. © 1998 John Wiley & Sons, Ltd.
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  • 179
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    Enzymatic Hydroxylation by Dopamine β-Hydroxylase (1998)
    Weinheim : Wiley-Blackwell
    Liebigs Annalen 1998 (1998), S. 1171-1176 
    Details
    ISSN: 1434-193X
    Keywords: Bioorganic chemistry ; Metalloenzymes ; Enzyme catalysis ; O-O activation ; C-H activation ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The three-dimensional aspects of the chemistry of dopamine β-hydroxylase (DBH) was studied through a conformationally-restricted substrate analog approach. We found that the DBH-catalyzed hydroxylation of 2-aminoindane (1) exclusively produced the trans-(1S,2S)-2-amino-1-indanol (4S) (93% ee) in contrast to the stereochemical course of the pro-R hydroxylation of the DBH/phenethylamine reaction. Studies with stereospecifically deuterium labeled 2-aminoindanes 2 and 3 show that the production of (1S)-aminoindanol 4S is the result of stereospecific pro-S hydrogen abstraction followed by the oxygen binding with overall retention of configuration. On the basis of these findings, we propose a model for the interaction of the phenethylamine substrates with the enzyme.
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    Alkoxycarbonylcarbene Transfer to Semicyclic Enaminones - A Route to Cyclopenta[b]pyrrole and Indole Ring Systems (1998)
    Weinheim : Wiley-Blackwell
    Liebigs Annalen 1998 (1998), S. 1177-1187 
    Details
    ISSN: 1434-193X
    Keywords: Diazo compounds ; Carbenes ; Heterocycles ; Enaminones ; Indoles ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Copper-catalyzed decomposition of alkyl diazoacetates in the presence of semicyclic enaminones 1a-o leads primarily to enamino esters 2 which constitute formal products of C-C insertion of the carbene unit. In the case of N-methyl (1a-e) and N-benzyl (1f-i) enaminones, 2a-i are accompanied by 2,3,5,6-tetrahydroindoles 3a-i, in which two carbene moieties are incorporated. At 250 °C, compounds 2b-e, which could not be isolated in pure form, undergo cyclocondensation to form 1,2,3,5-tetrahydrocyclopenta-[b]pyrroles 4b-e. In contrast, 2f-i can be isolated as Z,E mixtures and are transformed thermally into 4f-i only in the presence of silica gel. Carbene transfer to N-phenyl enaminones 1j-m and N-methyl enamino esters 1n,o leads only to the 1:1 adducts, enamino esters 2j-o, which do not undergo the cyclocondensation reaction under the previous conditions. Dehydrogenation of tetrahydroindoles 3c-e with tetrachloro-p-benzoquinone can be controlled to give either 1,2-dihydroindole-6,7-dicarboxylates 5 or indole-6,7-dicarboxylates 6.
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    Generation of 6,7-Dihydro-5H-1,3,4-thiadiazolo[3,2-a]pyridines  -  Unexpected Products in the Reaction of 5-Ethylthio-1,3,4-thiadiazole-2-amine and 3-(Dimethylamino)propiophenones (1998)
    Weinheim : Wiley-Blackwell
    Liebigs Annalen 1998 (1998), S. 1201-1203 
    Details
    ISSN: 1434-193X
    Keywords: 1,3,4-Thiadiazoles ; Pyridines ; Cyclizations ; Heterocycles ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A series of 6,8-diaroyl-6,7-dihydro-5H-1,3,4-thiadiazolo[3,2-a]pyridines 4a-e was prepared by the reaction of 5-ethylthio-1,3,4-thiadiazole-2-amine (1) and p-substituted 3-(dimethylamino)propiophenones 2a-e in pyridine. The unexpected cyclization process was established by NMR and X-ray diffraction measurements.
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  • 182
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    Cameroonane, Prenopsane and Nopsane, Three New Tricyclic Sesquiterpene Skeletons (1998)
    Weinheim : Wiley-Blackwell
    Liebigs Annalen 1998 (1998), S. 1205-1212 
    Details
    ISSN: 1434-193X
    Keywords: New tricyclic sesquiterpene alcohols ; Natural products ; Essential oil ; Compositae ; Odoriferous substances ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The strong patchouli-like and woody smelling essential oil of the rhizomes of Echinops giganteus var. lelyi C. D. Adams (Compositae) contains only sesquiterpenes, which are mainly triquinanes. Besides the known tricyclic compounds, silphiperfol-5- (1, 3) and -6-ene (4), modhephen-2-ene (5), α- (6) and β-isocomene (7), silphiperfolan-7β-ol (12), presilphiperfolan-8-ol (13), silphiperfol-6-en-5-one (14) and 7-epi-silphiperfolan-6β-ol (20), the following compounds, three of which (15, 17, 18) have new skeletons, were found, for the first time, occurring naturally: presilphiperfol-7-ene (2), cameroonan-7-ol (15), an 11(7→8)-abeo-presilphiperfolan-7-ol, prenopsan-8-ol (17), a 1(8→7)-abeo-cameroonan-8-ol, and nopsan-4-ol (18), a 3(4→8)-abeo-prenopsan-4-ol, three diastereomers of silphiperfolan-6-ol (19, 21, 22), modheph-2-en-8-ol (23) and silphiperfola-4,7(14)-diene (24). All structures were elucidated by NMR spectroscopy. A biogenetic pathway from a presilphiperfolane cation C to the cameroonane K, prenopsane L and nopsane M cations is shown. Cameroonanol (15) and prenopsanol (17) are the main contributors to the fragrance of the total oil.
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    Activation of Glycosyl Phosphites under Neutral Conditions in Solutions of Metal Perchlorates in Organic Solvents (1998)
    Weinheim : Wiley-Blackwell
    Liebigs Annalen 1998 (1998), S. 1227-1230 
    Details
    ISSN: 1434-193X
    Keywords: Glycosides ; Glycosylations ; Glycosyl phosphites ; Metal perchlorates ; LiClO4-solvent mixtures ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Glycosyl phosphites 1-3 derived from glucose are activated under neutral conditions and without the addition of any further promoter in 1 M solutions of LiClO4, Mg(ClO4)2 or Ba(ClO4)2 in ether, CH2Cl2, or CH3CN and react under these conditions with the alcohols5-9 to give the glycosides 10-14. The best results are obtained in the presence of Ba(ClO4)2. In CH2Cl2 and ether the α-anomers predominate, in CH3CN the β-isomers are formed in excess. Whereas the methyl phosphite 1 and the benzyl phosphite 3 deliver the desired glycosides in yields of 35-66%, the ethyl phosphite 2 is a more reactive glycosyl donor, giving the glycosides 10, 11 and 13 in 62-95% yield.
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    Synthesis and Properties of a Bis(2-buteno)-Bridged Bis(adamantane): X-ray and Molecular Dynamic Studies of the trans, trans Isomer (1998)
    Weinheim : Wiley-Blackwell
    Liebigs Annalen 1998 (1998), S. 1231-1236 
    Details
    ISSN: 1434-193X
    Keywords: Bis(adamantane), bis(2-buteno)-bridged ; Synthesis ; Molecular dynamic studies ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The synthesis of the trans,trans isomer of the bis(2-buteno)-bridged bis(adamantane) 3 has been developed, and its structure was established by spectral and X-ray structure analysis. Since the results of dynamic NMR studies indicate that 3 is conformationally mobile and the transition-state free energy (ΔGc≠) required to interconvert two equivalent con-formers was estimated to be ca. 60 kJ mol-1, the lowest energy conformer was subjected to a molecular dynamic simulation at 323 K in the gas phase. Three conformations 3a, 3b and 3c were found. The conformations 3a and 3c have anti-oriented adamantane units, while in 3b the adamantane molecules occupy the syn conformation. By analysing the conformational processes in macrocyclic diene 3, it was found that the calculated conformation 3a with molecular symmetry of C2h is very close to that found in solution at -50 °C, but differs from that which was observed in the solid state by X-ray-crystallographic analysis.
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    Repair of UV Light Induced DNA Lesions: A Comparative Study with Model Compounds (1998)
    Weinheim : Wiley-Blackwell
    Liebigs Annalen 1998 (1998), S. 1245-1258 
    Details
    ISSN: 1434-193X
    Keywords: UV irradiation ; DNA repair ; DNA photolyase ; Flavin ; Deazaflavin ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: DNA photolyases are enzymes that catalyze the light-dependend repair of cis-syn-cyclobutane-thymine dimer UV lesions in a variety of organisms. The basis of the repairreaction is an electron transfer from a reduced and deprotonated flavin cofactor to the dimer unit, which splits spontaneously as its radical anion. A second cofactor, which is either an 8-hydroxy-5-deazaflavin or a methenyl-tetrahydrofolate is required as a photo antenna and ensures efficient light absorption. With the help of model compounds that are able to mimic all crucial steps of the repair reaction, detailed mechanistic insights into the repair reaction could be obtained. It became clear, that the enzyme requires the reduced flavin in its deprotonated form and that the repair reaction proceeds most efficiently in polar media, which is in agreement with the observed highly polar flavin binding pocket. Investigations with flavin- and deazaflavin-containing model compounds confirmed that the deazaflavin functions solely as a photo antenna and allowed to study the dependencies of the antenna function on the protonation state of the 8-hydroxy-5-deazaflavin. The ability to mimic the repair reaction with small model compounds allowed finally the development of flavin cofactor functionalized oligo-peptides. Cofactor peptides with the sequence of the DNA-binding domain of the transcription factor MyoD were shown to be able to repair UV light lesions of DNA within a DNA single strand.
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    Synthesis of Bis[di(2-pyridyl)methyl]amine (BDPMA) by a Novel One-Pot Multi-Step Reductive Amination with Molecular Sieves and Zn/iPrOH (1998)
    Weinheim : Wiley-Blackwell
    Liebigs Annalen 1998 (1998), S. 1271-1273 
    Details
    ISSN: 1434-193X
    Keywords: Reductive amination ; Zinc ; Pentadentate ligand ; Polypyridine ligand ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Bis[di(2-pyridyl)methyl]amine (BDPMA) has been syn-thesized by refluxing di-2-pyridyl ketone and di-(2-pyridyl)methylamine in isopropanol in the presence of molecular sieves and acetic acid and subsequent reduction with zinc dust. The established methods for reductive amination, i.e. NaBH3CN, NaBH(OAc)3 and NaBH4, failed in the synthesis of BDPMA due to a disfavored equilibrium towards the imine formation and therefore long reaction times were required, involving side reactions. The presented method can be used on large-scales and tolerates aromatic heterocycles as functional groups.
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    Amino-Functionalized, Second-Generation Dendritic Building Blocks (1998)
    Weinheim : Wiley-Blackwell
    Liebigs Annalen 1998 (1998), S. 1275-1283 
    Details
    ISSN: 1434-193X
    Keywords: Dendrimers ; Amino-functionalized dendrons ; Building blocks ; Protecting groups, orthogonal ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The multi-gram scale synthesis of first- and second-generation dendrons with Boc- and Cbz-protected amino groups in the periphery and methyl/ethyl esters at the focal points is described. Saponification of the esters and deprotection of the amines are shown to be strictly orthogonal processes which makes these dendrons valuable building blocks for future constructions.
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    Insect-Plant Interactions - Metabolism of Plant Compounds to Pheromones and Allomones by Lepidoptera and Leaf Beetles (1998)
    Weinheim : Wiley-Blackwell
    Liebigs Annalen 1998 (1998), S. 13-20 
    Details
    ISSN: 1434-193X
    Keywords: Pyrrolizidine alkaloids ; Male pheromones ; Butterflies ; Chrysomelidae ; Insect defence ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Pyrrolizidine alkaloids are taken up from plants by various butterflies and moths belonging to the Danainae, Ithomiinae, and Arctiidae, which use them for defence and for the production of male pheromones. A complex distribution scheme of these plant alkaloids by the insect has been established in some species. The transformations involved include conversion into insect alkaloids, metabolism to male pheromones, and transfer of alkaloids from males to females and further into eggs. While these lepidoptera selectively sequester certain compounds from plants in a complex pattern, the leaf beetle Chrysomela lapponica follows a different strategy. Glycosidically bound alcohols present in leaves of their hostplants are liberated and transformed into esters, which are used for defence. Related beetles rely on host-derived single compounds such as salicyl aldehyde or de novo synthesized iridoid monoterpenes. Several aspects of these insect-plant relations, including biosynthetic transformations of plant compounds by the insects, are discussed herein.
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    Polymer-Supported Catalytic Asymmetric Sharpless Dihydroxylations of Olefins (1998)
    Weinheim : Wiley-Blackwell
    Liebigs Annalen 1998 (1998), S. 21-27 
    Details
    ISSN: 1434-193X
    Keywords: Heterogeneous catalysis ; Homogeneous catalysis ; Asymmetric catalysis ; Dihydroxylation ; Polymers ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The need for catalyst systems for the asymmetric dihydroxylation of olefins (AD) that combine the positive characteristics of the original homogeneous osmium catalysts with the ease of separation of heterogeneous catalysts led to the introduction of polymer-supported alkaloid ligands. Two major strategies for ligand recovery will be discussed here: (a) Attachment of the alkaloids to a solid support, such as an organic polymer or silica gel. After catalysis the ligands can easily be recycled by simple filtration. (b) The alkaloids are anchored to a polymeric unit which allows catalysis to be performed under homogeneous conditions. After the reaction is complete, the ligand is isolated by precipitation upon addition of solvent followed by filtration. Recent results of investigations of both strategies will be presented.
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    Synthesis of Phyllanthurinolactone, the Leaf-Closing Factor of Phyllanthus urinaria L., and Its Three Stereoisomers (1998)
    Weinheim : Wiley-Blackwell
    Liebigs Annalen 1998 (1998), S. 57-62 
    Details
    ISSN: 1434-193X
    Keywords: Aquilegiolide ; Glycosides ; Lactones ; Leaf-closing factor ; Menisdaurilide ; Phyllanthus urinaria L. ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Phyllanthurinolactone (1) and its three stereoisomers 18-20 were synthesized, and only 1 was bioactive as the leaf-closing factor of a nyctinastic plant, Phyllanthus urinaria L. X-ray analysis of the tetraacetylglucoside 17 was executed, and the absolute configuration of 1 was determined as 6S,7aR.
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    1-Vinyltricyclo[4.1.0.02,7]heptanes: Synthesis and Reactions with Electrophilic Dienophiles (1998)
    Weinheim : Wiley-Blackwell
    Liebigs Annalen 1998 (1998), S. 29-41 
    Details
    ISSN: 1434-193X
    Keywords: Strained molecules ; 1-Vinyltricyclo[4.1.0.02,7]heptanes ; Electrophilic additions ; Rearrangements ; Cyclic ketene imine ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A series of 1-vinyltricyclo[4.1.0.02,7]heptanes 4 has been obtained by Ni0-catalyzed cross-coupling reactions of the corresponding Grignard reagent with vinyl halides or via reaction of 4b with various electrophiles. Selected model compounds 4 were treated with tetracyanoethylene (TCNE), N-phenyl-1,2,4-triazoline-3,5-dione (PTAD), and dimethyl acetylenedicarboxylate (DMAD). Product studies revealed that TCNE and PTAD attacked the CC double bond forming a zwitterion, which in most cases underwent several carbenium ion rearrangements until internal bond formation of the ionic centers took place. The main reaction path of DMAD and 4 led via attack at the bicyclo[1.1.0]butane bridgehead to a biradical of type 38, which after H abstraction and CC bond formation gave rise to the tricyclic system 37.
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    Palladium(0)- and Nickel(0)-Catalyzed [3 + 2] Co-Cyclization Reactions of Bicyclopropylidene with Alkenes (1998)
    Weinheim : Wiley-Blackwell
    Liebigs Annalen 1998 (1998), S. 113-119 
    Details
    ISSN: 1434-193X
    Keywords: Bicyclopropylidene ; [3 + 2] Co-cyclization ; Nickel(0) catalysis ; Palladium(0) catalysis ; 4-Methylenespiro[2.4]heptane derivatives ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Bicyclopropylidene (1) readily undergoes a palladium(0)-catalyzed [3 + 2] co-cyclization with electron deficient alkenes (methyl acrylate, methyl trans-crotonate, methyl cinnamate and diethyl fumarate) as well as with some strained alkenes (norbornene, norbornadiene) by distal ring cleavage of one of the three-membered rings of 1. All these co-cyclizations are regioselective with respect to 1 as well as regio- and stereoselective with respect to the alkenes to give the corresponding 4-methylenespiro[2.4]heptane-trans-6-carboxylates 2a-5 with the electron deficient alkenes and the cycloadducts 6 and 7 with the strained alkenes in acceptable to good yields (56 to 83%). In contrast to palladium(0) catalysts nickel(0) complexes catalyze both distal ring opening of 1 and oxidative coupling of the two double bonds when 1 is reacted with e.g. diethyl fumarate. The result is a mixture of the methylenecyclopentane derivative 5 with the [2 + 2] cycloadduct 8 and the cotrimer 9.
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  • 193
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    Electronic Resource
    Kinetics of Strain-Activated Intramolecular Diels-Alder Reactions Between Furan and Bicyclopropylidene as well as Methylenecyclopropane Moieties (1998)
    Weinheim : Wiley-Blackwell
    Liebigs Annalen 1998 (1998), S. 107-112 
    Details
    ISSN: 1434-193X
    Keywords: Cycloadditions, intramolecular, [4 + 2] ; Strain activation ; High-pressure chemistry ; Polycycles ; Small ring systems ; Volume profile ; Activation parameters ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The intramolecular Diels-Alder reactions of the furans 1a, 1b, 3a and 3b in dichloromethane solution at pressures up to 3 kbar have been studied by quantitative on-line FT-IR spectroscopy. At identical pressure and temperature cyclization rates are significantly faster, by a factor of 8.1 and 6.8, for the b-type species of 1 and 3, respectively. The activation enthalpies of the four cyclizations are very similar, between 78.5 ± 0.6 and 82.5 ± 2.7 kJ mol-1. The activation volumes, ΔV0≠, are in the range -28.4 ± 1.3 (1a) to -40.8 ± 2.0 cm3 mol-1 (3b). These data show that intramolecular Diels-Alder reactions are not necessarily associated with less negative activation volumes than intermolecular Diels-Alder reactions. The size of ΔV0≠, however, appears to be clearly correlated with the type and the position of substituents at the diene or dienophile moieties. Replacement of the H atom on the furan ring by the methoxy group turns ΔV0≠ more negative by 7.4 ± 2.9 cm3 mol-1 for 1a and 1b and by 8.1 ± 2.0 cm3 mol-1 for 3a and 3b. Varying the dienophile moiety from methylenecyclopropane to bicyclopropylidene lowers ΔV0≠ by about 3.5 cm3 mol-1 between 1a and 3a and by about 5.0 cm3 mol-1 between 1b and 3b, which demonstrates the larger steric hindrance due to the tetrasubstitution of the double bond. Comparing the effects on cyclization rate associated with having either one or two cyclopropane units at the dienophile double bond suggests that the rate enhancing influence of strain energy slightly overcompensates a reduction in rate that is expected to go with the increased steric hindrance due to the second cyclopropane unit.
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  • 194
    Electronic Resource
    Electronic Resource
    Nitrogen-Rich Mesoionic Compounds from 1,3-Diaryl-5-chlorotetrazolium Salts and Nitrogen Nucleophiles - Synthesis and Properties of 1,3-Diaryl-5-azidotetrazolium Salts (1998)
    Weinheim : Wiley-Blackwell
    Liebigs Annalen 1998 (1998), S. 121-127 
    Details
    ISSN: 1434-193X
    Keywords: Azides ; Betaines ; Carbenes ; Nitrogen heterocycles ; Nucleophilic aromatic substitution ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Nitrogen-rich mesoions have been synthesized by the reaction of the 5-chloro-1,3-diaryltetrazolium salt 1 with various nitrogen nucleophiles. The reactions with aqueous ammonia and hydroxylamine gave tripolar mesoionic amide 2 and mesoionic hydroxylamide 4, respectively. N-Substituted and N,N-disubstituted hydrazines yielded the corresponding hydrazides 5, whereas N,N-diphenylhydrazine gave the rearranged product 6. The reaction with sodium azide gave 5-azidotetrazolium salt 8. The azido group of 8 was reduced to give aminotetrazolium salt 9, deprotonation of which yielded the corresponding conjugate base 3. Hard nucleophiles attacked the tetrazolium carbon atom of 8 to give substitution products, whereas soft nucleophiles added the terminal nitrogen atom of the azido group to give addition products. Azidotetrazolium salt 8 reacted further with sodium azide to give a high yield of the tetrazol derivative 11, together with a small amount of triazene 17. The intermediacy of mesoionic carbene 19 is postulated.
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  • 195
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    Electronic Resource
    Isolation and Structure of Three New Ceramides from the Starfish Acanthaster planci (1998)
    Weinheim : Wiley-Blackwell
    Liebigs Annalen 1998 (1998), S. 129-131 
    Details
    ISSN: 1434-193X
    Keywords: Sphingolipids ; Ceramides ; Starfish ; Acanthaster planci ; FABMS/MS ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Three new phytosphingosine-type ceramides, AC-1-6, AC-1-10 and AC-1-11, were isolated from the ceramide molecular species AC-1, obtained from the less polar fraction of the CHCl3-MeOH extract of the starfish Acanthaster planci. The structures of these ceramides were determined on the basis of chemical and spectroscopic evidence as (2S,2′R,3S,4R,9Z)-2-(2-hydroxyhexadecanoylamino)-9-docosene-1,3,4-triol (AC-1-6), (2S,2′R,3S,4R,)-2-(2-hydroxytricosanoylamino)hexadecane-1,3,4-triol (AC-1-10) and (2S,2′R,3S,4R,)-2(2-hydroxytetracosanoylamino)hexadecane-1,3,4-triol (AC-1-11). Positive ion FABMS/MS of each ceramide gave important information for their structure elucidation. Mass spectrometry of the dimethyl disulfide derivatives of ceramide was also useful for the determination of the double bond position in the long-chain base.
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  • 196
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    Electronic Resource
    Unprecedented 1,3-Dipolar Cycloaddition of Azomethine Ylides Derived from Difluorocarbene and Imines to Carbonyl Compounds. - Synthesis of Oxazolidine Derivatives (1998)
    Weinheim : Wiley-Blackwell
    Liebigs Annalen 1998 (1998), S. 133-137 
    Details
    ISSN: 1434-193X
    Keywords: Azomethine ylides ; Difluorocarbene ; Cycloadditions ; Heterocycles ; Oxazolidines ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Iminiodifluoromethanides generated by the reaction of difluorocarbene with benzaldehyde and benzophenone imines undergo regioselective 1,3-dipolar cycloaddition to aldehydes to give oxazolidine derivatives.
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  • 197
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    Electronic Resource
    Synthesis and Photocyclization of Macrocyclic Stilbene Derivatives (1998)
    Weinheim : Wiley-Blackwell
    Liebigs Annalen 1998 (1998), S. 149-154 
    Details
    ISSN: 1434-193X
    Keywords: Cyclophanes ; McMurry reaction ; Phenanthrenes ; Photochemistry ; Pinacol coupling ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The stereoselectivity of the formation of macrocyclic stilbenes as well as the regioselectivity of their photocyclization are strongly influenced by the length of the connecting alkanediyl chain. The stereoisomers of the macrocyclic stilbenes and the corresponding diols are identified by chemical and spectroscopic means.
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  • 198
    Electronic Resource
    Electronic Resource
    Distance Dependence of Photoinduced Electron Transfer: Syntheses and Properties of Anthracene-Spacered Porphyrin-Quinone Cyclophanes (1998)
    Weinheim : Wiley-Blackwell
    Liebigs Annalen 1998 (1998), S. 631-642 
    Details
    ISSN: 1434-193X
    Keywords: Electron transfer, distance dependence of ; Anthracene-spacered porphyrin-quinone cyclophanes ; Syntheses ; Characterizations ; Structures ; Physical properties ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In our previous work on benzene- and naphthalene-spacered porphyrin-quinone cyclophanes[1][2], the dependence of electron-transfer rates on reduction potentials of the acceptors and oxidation potentials of the porphyrins was studied. The present paper, dealing with the distance dependence of electron transfer, reports on the synthesis of anthracene-spacered analogues and on the electron-transfer rates, which are found to be drastically reduced.
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  • 199
    Electronic Resource
    Electronic Resource
    The Barrier to Rotation about the Double Bond in Methylenecyclopropane (1998)
    Weinheim : Wiley-Blackwell
    Liebigs Annalen 1998 (1998), S. 763-768 
    Details
    ISSN: 1434-193X
    Keywords: Pyramidalization ; Rotational barrier ; Strained molecules ; Propellanes ; Small-ring systems ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Activation parameters have been determined in the gas phase for the geometrical isomerization of the double bonds in two phenyl-substituted methylenecyclopropanes (2 and 8). Comparison with the analogous values for three sterically non-restricted styrene derivatives (15, 16 and 17) shows that the enthalpies of activation for the methylenecyclopropanes are lower by 3.7 kcal mol-1. This value, which is an upper limit to the amount of strain energy released by pyramidalization of the ring carbon atom in the orthogonal diradical transition state when undergoing geometrical isomerization, is considerably smaller than the value of 12-14 kcal mol-1 by which the strain energy of methylenecyclopropane is larger relative to that of cyclopropane. Our kinetics experiments thus show that the angle strain, associated with incorporating a trigonal carbon atom into the three-membered ring, is not responsible for the majority of the additional strain energy of methylenecyclopropane, relative to that of cyclopropane.
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  • 200
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    Electronic Resource
    Total Synthesis of TAN-1057 A/B, a New Dipeptide Antibiotic from Flexibacter sp. PK-74 (1998)
    Weinheim : Wiley-Blackwell
    Liebigs Annalen 1998 (1998), S. 777-783 
    Details
    ISSN: 1434-193X
    Keywords: Antibiotics ; Dipeptides ; Heterocycles ; β-Amino acid ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: TAN-1057 (1a, b) - a new natural dipeptide antibiotic active against methicillin resistant strains of Staphylococcus aureus - was synthesized starting from Nα, Nδ, Nω-tri-Z-L-arginine 20b via the corresponding diazoketone 21b. This upon photolysis rearranged to the ketene which was trapped by (±)-2,4,5,6-tetrahydro-5-methylamino-2-ureidopyrimidin-4-one (3) to yield the fully protected dipeptide 23 (30%). The latter was deprotected by hydrogenolysis to give the final compound as a mixture of two epimers - TAN-1057A, B - isolated previously from a strain of Flexibacter sp. PK-74. The intermediate 3 was prepared from 3-amino-2-(N-Z-N-methylamino)propionic acid methyl ester hydrochloride (16) and 2-methyl-2-thiopseudobiuret hydroiodide (18) in one step in 35% yield.
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