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  • 1990-1994  (3,320)
  • 1945-1949
  • 1920-1924
  • Engineering  (3,320)
  • 201
    Electronic Resource
    Electronic Resource
    Announcement (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 7 (1994), S. 307-307 
    Details
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jnm.1660070407
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  • 202
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    Electronic Resource
    Masthead (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 7 (1994) 
    Details
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jnm.1660070601
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  • 203
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    Electronic Resource
    Editorial (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994), S. 105-105 
    Details
    ISSN: 1070-5325
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nla.1680010202
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  • 204
    Electronic Resource
    Electronic Resource
    Properties of generalized conjugate gradient methods (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994), S. 45-63 
    Details
    ISSN: 1070-5325
    Keywords: Conjugate gradients ; Convergence ; Linear systems ; Acceleration of conjugate gradients ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The solution of linear systems has considerable importance for the computation of problems resulting from engineering, physics, chemistry, computer science, mathematics, medicine and economics. The calculation of costly and time-consuming problems, e.g. crash tests, simulation of the human lung and skin, calculation of electrical and magnetical fields, thermal analysis and fluid dynamics, to name only a few, has become possible with the recent developments of advanced computer architectures and iterative solvers. Generalized conjugate gradient (CG) methods are the most important iterative solvers because they converge very quickly under certain conditions. Therefore they are widely used and in a rapid further development.The purpose of this paper is to present new results for the convergence of generalized CG methods. A convergence result for non-symmetric and non-positive definite matrices is given that includes the classical theory for symmetric, positive definite matrices as a special case.The norm of the residuals resulting from CG methods may oscillate heavily. Different remedies for smoothing this sequence have been proposed, for example by van der Vorst. Schönauer introduced in the 1980s a smoothing algorithm to get a norm nonincreasing function of the iteration index. For this algorithm a complete theoretical analysis is given. A surprising result is obtained showing that the smoothing algorithm is in a sense optimal. Convergence estimates are derived therefrom. A geometric interpretation of the smoothing algorithm is given showing the propagation of the errors.It should be stressed that a smooth convergence of the residuals is not equivalent to a smooth convergence of the errors which is the proper aim. A class of error minimizing methods can be easily derived from the theory.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nla.1680010106
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  • 205
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    Electronic Resource
    Displacement decomposition - incomplete factorization preconditioning techniques for linear elasticity problems (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994), S. 107-128 
    Details
    ISSN: 1070-5325
    Keywords: Incomplete factorization ; Preconditioning ; Linear elasticity problems ; Displacement decomposition ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Two preconditioning techniques for the numerical solution of linear elasticity problems are described and studied. Both techniques are based on spectral equivalence approach. The first technique consists in an incomplete factorization of the separate displacement component part of the stiffness matrix. The second technique uses an incomplete factorization of the isotropic approximation to the stiffness matrix. Results concerning existence, stability and efficiency of these preconditioning techniques are presented. The efficiency and robustness of the described techniques are illustrated by numerical experiments.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nla.1680010203
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  • 206
    Electronic Resource
    Electronic Resource
    The concept of special inner products for deriving new conjugate gradient-like solvers for non-symmetric sparse linear systems (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994), S. 129-139 
    Details
    ISSN: 1070-5325
    Keywords: Conjugate gradient method ; Nonsymmetric linear system ; Krylov subspace method ; Conjugate residual method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Yserentant's and Bramble/Pasciak/Xu's hierarchical preconditioners only require the hierarchical node connection of a finite element grid. So they could be applied to nonsymmetric FE-systems too, having a symmetric preconditioner. We investigate the question whether this fact could be useful in the CG-like iterative methods. The main key is the consideration of an appropriate choice of the inner product defined in the N-vector space. It is shown, how the inner product influences the formulas of the methods, the rate of convergence and some other properties.
    Additional Material: 7 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nla.1680010204
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  • 207
    Electronic Resource
    Electronic Resource
    Numerical calculation of invariant manifolds for maps (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994), S. 141-150 
    Details
    ISSN: 1070-5325
    Keywords: Invariant manifolds ; Error estimates ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Many processes in the sciences and in engineering are modelled by dynamical systems and - in discretized version - by nonlinear maps. To understand the often complicated dynamical behaviour it is a well established tool to use the concept of invariant manifolds of the system. In this way it is often possible to reduce the dimension of the system considerably. In this paper we propose a new method to calculate numerically invariant manifolds near fixed points of maps. We prove convergence of our procedure and provide an error estimation. Finally, the application of the method is illustrated by examples.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nla.1680010205
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  • 208
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    Equivalence of conditions for convergence of iterative methods for singular equations (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994), S. 151-154 
    Details
    ISSN: 1070-5325
    Keywords: Linear systems ; Singular systems ; Iterative methods ; Convergent methods ; Index of the iteration operator ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Equivalence is shown between different conditions for convergence of iterative methods for consistent singular systems of linear equations on Banach spaces. These systems appear in many applications, such as Markov chains and Markov processes. The conditions considered relate the range and null spaces of different operators.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nla.1680010206
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  • 209
    Electronic Resource
    Electronic Resource
    On the convergence of difference schemes for a heat conduction equation (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994), S. 237-245 
    Details
    ISSN: 1070-5325
    Keywords: Korovkin theorem ; Heat conduction equation ; Lax theorem ; Difference scheme ; Convergence ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Sufficient conditions are obtained for the convergence of difference schemes for the numerical solution of the Cauchy problem for a heat conduction equation in two space variables. The sufficient conditions are derived in a form similar to those for the convergence of a sequence of linear positive operators in the Korovkin theorem. As an application it is shown that difference schemes that are widely used in practice can easily be checked for convergence by these conditions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nla.1680010303
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  • 210
    Electronic Resource
    Electronic Resource
    Algebraic multilevel iteration method for Stieltjes matrices (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994), S. 213-236 
    Details
    ISSN: 1070-5325
    Keywords: Optimal order preconditioners ; Algebraic multilevel ; Chebyshev polynomial approximation ; Diagonal compensation ; Approximate inverses ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The numerical solution of elliptic selfadjoint second-order boundary value problems leads to a class of linear systems of equations with symmetric, positive definite, large and sparse matrices which can be solved iteratively using a preconditioned version of some algorithm. Such differential equations originate from various applications such as heat conducting and electromagnetics. Systems of equations of similar type can also arise in the finite element analysis of structures.We discuss a recursive method constructing preconditioners to a symmetric, positive definite matrix. An algebraic multilevel technique based on partitioning of the matrix in two by two matrix block form, approximating some of these by other matrices with more simple sparsity structure and using the corresponding Schur complement as a matrix on the lower level, is considered.The quality of the preconditioners is improved by special matrix polynomials which recursively connect the preconditioners on every two adjoining levels. Upper and lower bounds for the degree of the polynomials are derived as conditions for a computational complexity of optimal order for each level and for an optimal rate of convergence, respectively.The method is an extended and more accurate algebraic formulation of a method for nine-point and mixed five- and nine-point difference matrices, presented in some previous papers.
    Additional Material: 9 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nla.1680010302
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  • 211
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    Electronic Resource
    Masthead (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994) 
    Details
    ISSN: 1070-5325
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nla.1680010101
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  • 212
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    Editorial (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994), S. 1-1 
    Details
    ISSN: 1070-5325
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nla.1680010102
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  • 213
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    Low-rank revealing QR factorizations (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994), S. 33-44 
    Details
    ISSN: 1070-5325
    Keywords: Rank revealing QR factorization ; Column pivoting ; Numerical rank ; Subset selection ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Rank revealing factorizations are used extensively in signal processing in connection with, for example, linear prediction and signal subspace algorithms. We present an algorithm for computing rank revealing QR factorizations of low-rank matrices. The algorithm produces tight upper and lower bounds for all the largest singular values, thus making it particularly useful for treating rank deficient problems by means of subset selection, truncated QR, etc. The algorithm is similar in spirit to an algorithm suggested earlier by Chan for matrices with a small nullity, and it can also be considered as an extension of ordinary column pivoting.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nla.1680010105
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  • 214
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    On the use of two QMR algorithms for solving singular systems and applications in Markov chain modeling (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994), S. 403-420 
    Details
    ISSN: 1070-5325
    Keywords: Quasi-minimal residual iteration ; Non-Hermitian matrix ; Singular linear system ; Markov chain modeling ; Krylov-subspace method ; Convergence ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Recently, Freund and Nachtigal proposed the quasi-minimal residual algorithm (QMR) for solving general nonsingular non-Hermitian linear systems. The method is based on the Lanczos process, and thus it involves matrix - vector products with both the coefficient matrix of the linear system and its transpose. Freund developed a variant of QMR, the transpose-free QMR algorithm (TFQMR), that only requires products with the coefficient matrix. In this paper, the use of QMR and TFQMR for solving singular systems is explored. First, a convergence result for the general class of Krylov-subspace methods applied to singular systems is presented. Then, it is shown that QMR and TFQMR both converge for consistent singular linear systems with coefficient matrices of index 1. Singular systems of this type arise in Markov chain modeling. For this particular application, numerical experiments are reported.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nla.1680010406
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  • 215
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    Masthead (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994) 
    Details
    ISSN: 1070-5325
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nla.1680010501
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  • 216
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    ILUT: A dual threshold incomplete LU factorization (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994), S. 387-402 
    Details
    ISSN: 1070-5325
    Keywords: Preconditioning ; Incomplete LU ; Threshold strategies ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we describe an Incomplete LU factorization technique based on a strategy which combines two heuristics. This ILUT factorization extends the usual ILU(O) factorization without using the concept of level of fill-in. There are two traditional ways of developing incomplete factorization preconditioners. The first uses a symbolic factorization approach in which a level of fill is attributed to each fill-in element using only the graph of the matrix. Then each fill-in that is introduced is dropped whenever its level of fill exceeds a certain threshold. The second class of methods consists of techniques derived from modifications of a given direct solver by including a dropoff rule, based on the numerical size of the fill-ins introduced, traditionally referred to as threshold preconditioners. The first type of approach may not be reliable for indefinite problems, since it does not consider numerical values. The second is often far more expensive than the standard ILU(O). The strategy we propose is a compromise between these two extremes.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nla.1680010405
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  • 217
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    On the convergence behavior of the restarted GMRES algorithm for solving nonsymmetric linear systems (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994), S. 427-447 
    Details
    ISSN: 1070-5325
    Keywords: Nonsymmetric linear systems ; Conjugate gradient type iterative methods ; GMRES ; Restarting ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The solution of nonsymmetric systems of linear equations continues to be a difficult problem. A main algorithm for solving nonsymmetric problems is restarted GMRES. The algorithm is based on restarting full GMRES every s iterations, for some integer s〉0. This paper considers the impact of the restart frequency s on the convergence and work requirements of the method. It is shown that a good choice of this parameter can lead to reduced solution time, while an improper choice may hinder or preclude convergence. An adaptive procedure is also presented for determining automatically when to restart. The results of numerical experiments are presented.
    Additional Material: 4 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nla.1680010502
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  • 218
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    A comparison of some domain decomposition and ILU preconditioned iterative methods for nonsymmetric elliptic problems (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994), S. 477-504 
    Details
    ISSN: 1070-5325
    Keywords: Domain decomposition ; Preconditioning ; Iterative methods ; Nonsymmetric and/or indefinite elliptic problems ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In recent years, competitive domain-decomposed preconditioned iterative techniques of Krylov-Schwarz type have been developed for nonsymmetric linear elliptic systems. Such systems arise when convection-diffusion-reaction problems from computational fluid dynamics or heat and mass transfer are linearized for iterative solution. Through domain decomposition, a large problem is divided into many smaller problems whose requirements for coordination can be controlled to allow effective solution on parallel machines. A central question is how to choose these small problems and how to arrange the order of their solution. Different specifications of decomposition and solution order lead to a plethora of algorithms possessing complementary advantages and disadvantages. In this report we compare several methods, including the additive Schwarz algorithm, the classical multiplicative Schwarz algorithm, an accelerated multiplicative Schwarz algorithm, the tile algorithm, the CGK algorithm, the CSPD algorithm, and also the popular global ILU-family of preconditioners, on some nonsymmetric or indefinite elliptic model problems discretized by finite difference methods. The preconditioned problems are solved by the unrestarted GMRES method. A version of the accelerated multiplicative Schwarz method is a consistently good performer.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nla.1680010504
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  • 219
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    Parallel block preconditioning based on SSOR and MILU (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994), S. 533-553 
    Details
    ISSN: 1070-5325
    Keywords: Preconditioning ; MILU ; SSOR ; Finite difference discretization ; Convection-diffusion equation ; Parallel computer ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Two kinds of parallel preconditioners for the solution of large sparse linear systems which arise from the 2-D 5-point finite difference discretization of a convection-diffusion equation are introduced. The preconditioners are based on the SSOR or MILU preconditioners and can be implemented on parallel computers with distributed memories. One is the block preconditioner, in which the interface components of the coefficient matrix between blocks are ignored to attain parallelism in the forward-backward substitutions. The other is the modified block preconditioner, in which the block preconditioner is modified by taking the interface components into account. The effect of these preconditioners on the convergence of preconditioned iterative methods and timing results on the parallel computer (Cenju) are presented.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nla.1680010603
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  • 220
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    Approximate factorizations with modified S/P consistently ordered M-factors (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994), S. 3-17 
    Details
    ISSN: 1070-5325
    Keywords: M-matrices ; Preconditioning ; Incomplete factorizations ; Consistent orderings ; Matrix graphs ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Preconditioned iterative methods are widely used to solve linear systems such as those arising from the finite element formulation of boundary value problems and approximate factorizations are widely used as preconditioners. The ordering of the unknowns is therefore an important issue because it has a strong influence on the convergence behaviour of the iteration method while it is also a decisive aspect for their parallel implementation. Consistent orderings are attractive for parallel implementations and it has been shown that some subclasses of these orderings also enhance the convergence behaviour of the associated iteration methods. This has in particular been shown for the so-called S/P consistent orderings. A wider definition of this class of orderings has recently been proposed and we investigate here how approximate factorizations should be implemented when using such more general orderings (still called S/P consistent) in order to keep their expected high convergence properties. A simple practical conclusion is suggested, supported by both theoretical and numerical arguments.
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nla.1680010103
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  • 221
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    S/P images of upper triangular M-matrices (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994), S. 19-31 
    Details
    ISSN: 1070-5325
    Keywords: M-matrices ; Preconditioning ; Incomplete factorizations ; Consistent orderings ; Matrix graphs ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Preconditioning by approximate factorizations is widely used in iterative methods for solving linear systems such as those arising from the finite element formulation of many engineering problems. The influence of the ordering of the unknowns on their convergence behaviour has been the subject of recent investigations because of its particular relevance for the parallel implementation of these methods. Consistent orderings are attractive for parallel implementations and subclasses of these orderings have been shown to also enhance the convergence properties of the associated preconditioned iteration scheme. The present contribution is concerned with one such class of orderings, called S/P consistent orderings. More precisely, we review here their known properties and we propose a new definition which enlarges their scope of application. A device, called S/P image of an upper triangular M-matrix, provides a criterion for checking S/P consistency and a means to compute a relevant parameter, called maximal reduction ratio. All known properties of S/P consistent orderings are generalized to the new definition.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nla.1680010104
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  • 222
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    About the Front Cover (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994), S. 103-103 
    Details
    ISSN: 1070-5325
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nla.1680010109
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  • 223
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    Masthead (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994) 
    Details
    ISSN: 1070-5325
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nla.1680010201
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  • 224
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    Conference Diary (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994), S. 211-212 
    Details
    ISSN: 1070-5325
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nla.1680010209
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  • 225
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    New convergence results and preconditioning strategies for the conjugate gradient method (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994), S. 179-210 
    Details
    ISSN: 1070-5325
    Keywords: Linear system solvers ; Conjugate gradients ; Iteration number estimates ; Explicit preconditionings ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Instead of the standard estimate in terms of the spectral condition number we develop a new CG iteration number estimate depending on the quantity B = 1/ntr M/(det M)1/n, where M is an n × n preconditioned matrix. A new family of iterative methods for solving symmetric positive definite systems based on B-reducing strategies is described. Numerical results are presented for the new algorithms and compared with several well-known preconditioned CG methods.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nla.1680010208
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  • 226
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    Diagonally compensated reduction and related preconditioning methods (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994), S. 155-177 
    Details
    ISSN: 1070-5325
    Keywords: Preconditioning ; Diagonal compensation ; Eigenvalue bounds ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: When solving linear algebraic equations with large and sparse coefficient matrices, arising, for instance, from the discretization of partial differential equations, it is quite common to use preconditioning to accelerate the convergence of a basic iterative scheme. Incomplete factorizations and sparse approximate inverses can provide efficient preconditioning methods but their existence and convergence theory is based mostly on M-matrices (H-matrices). In some application areas, however, the arising coefficient matrices are not H-matrices. This is the case, for instance, when higher-order finite element approximations are used, which is typical for structural mechanics problems. We show that modification of a symmetric, positive definite matrix by reduction of positive offdiagonal entries and diagonal compensation of them leads to an M-matrix. This diagonally compensated reduction can take place in the whole matrix or only at the current pivot block in a recursive incomplete factorization method. Applications for constructing preconditioning matrices for finite element matrices are described.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nla.1680010207
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  • 227
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    Electronic Resource
    Masthead (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994) 
    Details
    ISSN: 1070-5325
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nla.1680010301
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    Masthead (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994) 
    Details
    ISSN: 1070-5325
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nla.1680010401
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    On the use of periodicity properties for the efficient numerical solution of certain Markov chains (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994), S. 265-286 
    Details
    ISSN: 1070-5325
    Keywords: Continuous and discrete-time Markov chains ; P-cyclic graph structure ; Reduced schemes ; Numerical solution methods ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Markov chains with periodic graphs arise frequently in a wide range of modelling experiments. Application areas range from flexible manufacturing systems in which pallets are treated in a cyclic manner to computer communication networks. The primary goal of this paper is to show how advantage may be taken of this property to reduce the amount of computer memory and computation time needed to compute stationary probability vectors of periodic Markov chains. After reviewing some basic properties of Markov chains whose associated graph is periodic, we introduce a ‘reduced scheme’ in which only a subset of the probability vector need be computed. We consider the effect of the application of both direct and iterative methods to the original Markov chain (permuted to normal periodic form) as well as to the reduced system. We show how the periodicity of the Markov chain may be efficiently computed as the chain itself is being generated. Finally, some numerical experiments to illustrate the theory, are presented.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nla.1680010305
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    Editorial (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994), S. 335-335 
    Details
    ISSN: 1070-5325
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nla.1680010402
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    GMRESR: a family of nested GMRES methods (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994), S. 369-386 
    Details
    ISSN: 1070-5325
    Keywords: GMRES ; Unsymmetric linear systems ; Iterative solver ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Recently Eirola and Nevanlinna have proposed an iterative solution method for unsymmetric linear systems, in which the preconditioner is updated from step to step. Following their ideas we suggest variants of GMRES, in which a preconditioner is constructed per iteration step by a suitable approximation process, e.g., by GMRES itself. Our numerical experiments indicate that this may lead to considerable savings in CPU-time and memory requirements in typical CFD applications.
    Additional Material: 10 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nla.1680010404
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    Local refinement techniques for elliptic problems on cell-centered grids; II. Optimal order two-grid iterative methods (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994), S. 337-368 
    Details
    ISSN: 1070-5325
    Keywords: Local refinement ; Preconditioning ; Two-grid method ; Cell-centered grids ; Finite differences ; Elliptic problem ; Optimal rate of convergence ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Two preconditioning techniques for solving difference equations arising in finite difference approximation of elliptic problems on cell-centered grids are studied. It is proven that the BEPS and the FAC preconditioners are spectrally equivalent to the corresponding finite difference schemes, including a nonsymmetric one, which is of higher-order accuracy. Numerical experiments that demonstrate the fast convergence of the preconditioned iterative methods (CG and GCG-LS in the nonsymmetric case) are presented.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nla.1680010403
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    Conference diary (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994), S. 421-425 
    Details
    ISSN: 1070-5325
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nla.1680010407
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    On the roots of the orthogonal polynomials and residual polynomials associated with a conjugate gradient method (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994), S. 449-475 
    Details
    ISSN: 1070-5325
    Keywords: Orthogonal ; polynomials ; Residual polynomials ; Conjugate ; gradient ; method ; Ritz values ; Field of values ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we explore two sets of polynomials, the orthogonal polynomials and the residual polynomials, associated with a preconditioned conjugate gradient iteration for the solution of the linear system Ax = b. In the context of preconditioning by the matrix C, we show that the roots of the orthogonal polynomials, also known as generalized Ritz values, are the eigenvalues of an orthogonal section of the matrix C A while the roots of the residual polynomials, also known as pseudo-Ritz values (or roots of kernel polynomials), are the reciprocals of the eigenvalues of an orthogonal section of the matrix (C A)-1. When C A is selfadjoint positive definite, this distinction is minimal, but for the indefinite or nonselfadjoint case this distinction becomes important. We use these two sets of roots to form possibly nonconvex regions in the complex plane that describe the spectrum of C A.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nla.1680010503
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    Conference Diary (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994), S. 505-509 
    Details
    ISSN: 1070-5325
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nla.1680010505
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    Masthead (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994) 
    Details
    ISSN: 1070-5325
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nla.1680010601
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  • 237
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    Generalized finite-differences solution of 3D elliptical problems involving Neumann boundary conditions (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 43-58 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method is presented for the solution of elliptical problems defined on general-shape multiconnected three-dimensional domains approximated by means of polyhedra. The boundary conditions may be of the Neumann type. The differential operator and the normal derivative are discretized by generalized finite-difference (GFD) methods using an orthogonal non-uniform Cartesian grid. The convergence properties are analysed and the solutions of some Poisson and biharmonic problem are presented.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640100106
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  • 238
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    Heuristic optimization of a laminated composite plate and its comparison with a minimization method (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 59-65 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A heuristic optimization design methodology based on redesign rules for composite laminated plates is presented. It is modelled on the cyclic approach to the design process observed in designers of structural components using composites. In comparison with a simple weight minimization algorithm it gives quasioptimal ply thicknesses, but takes under ten iterations. It is thereby shown to be most suitable for initial design studies. Multiaxial combinations of in-plane loads and bending moments are considered in the design procedure.
    Additional Material: 5 Tab.
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    URL: http://dx.doi.org/10.1002/cnm.1640100107
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    Numerical investigation of a method to reduce the reheating time of steel bars (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 33-42 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Reduction of reheating time saves on energy input and increases the production rate in the steel-making process. Reductions can be achieved by allowing the centre temperature of a steel bar to be lower than the surface temperature by a small margin, before starting with the hot rolling process. This can only be done if the temperature difference does not adversely affect the quality of the final product or the rolling equipment. The paper presents numerical simulations to investigate the savings that can be obtained for various temperature differences between surface and centre temperatures to evaluate the feasibility of the concept. The results presented include the cross-sectional temperature distribution in a typical steel bar during reheating at hourly intervals as well as the effect of various differences between centre and surface temperatures on reheating time. The reheating time predicted for various steel bar sizes as well as for various differences between surface and centre temperatures are then compared against measured reheating times. To indicate the practical applicability of the concept to the hot rolling process the detailed temperature distribution in a typical steel bar, with an initial temperature difference between the surface and centre of the bar, was simulated numerically. This was compared to a similar simulation for a well soaked steel bar for which experimental measurements are also available. The numerical method used to obtain the simulations is also presented. Boundary conditions account for radiation, convection and conduction inside the steel bar. It is concluded that the concept of allowing differences between surface and centre temperatures of a steel bar during reheating holds great potential for energy savings in the steel-making process.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640100105
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    Higher-order singular isoparametric elements for crack problems (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 73-80 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Standard isoparametric finite elements can be used as singular crack-tip elements in fracture mechanical computations by placing the middle nodes in the neighbourhood of the crack tip. Such elements have already been applied to several plane and three-dimensional problems, so this method can be considered as commonly well accepted. The paper shows that singularity of order r(1 - m)/m is obtained with an nth-order isoparametric element.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640100109
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    Method of iterative linearization to solve non-linear stochastic vibration problems (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 67-71 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, an iterative method of statistic linearization (IMSL) is presented to solve non-linear stochastic vibration equations. This method represents an improvement over the classical linearization method. The method uses the solution of the corresponding linear vibration equation as an initial value in an iterative procedure. To obtain information about essential statistical average values, the method uses a ‘boot-strapping’ procedure, which defines a pseudorandom process based on the statistical characteristics of the linear solution and then uses samples from the process to estimate them. For Gaussian input excitation, the statistical average values are obtained by theoretical analysis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640100108
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  • 242
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    Conference diary (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 89-91 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640100111
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  • 243
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    BEM computation of DSIF in cracked viscoelastic plates (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 81-87 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Dynamic stress intensity factors of cracked linear viscolastic solids under conditions of plane stress are computed by the boundary-element method in conjunction with the numerical Laplace transform and the correspondence principle of linear viscoelasticity. Quadratic isoparametric conventional and quarter-point boundary elements are employed. The multidomain approach is used in cases where symmetry cannot be invoked. Dynamic stress intensity factors are computed for cracked viscoelastic rectangular plates subjected to suddenly applied loads, and comparisons are made against results obtained by other numerical methods.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640100110
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  • 244
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    Masthead (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994) 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640100201
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  • 245
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    Compound difference schemes for time-dependent equations on non-uniform nets (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 93-110 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new approach to constructing monotonous second-order-accurate schemes for time-dependent Navier-Stokes equations in the compressible case is suggested. Flows with shock waves and thin viscous boundary layers are considered. The approach joins two different schemes while each of them is appropriate for its own type of flow. The resulting scheme is constructed as a splitting one, and the approach is applied at the stage governed by the Euler equations in Lagrangian variables. The approach turns out to be fruitful also for parabolic equations with ‘viscous’ terms. The method is illustrated by the problem on compression of deuterium in a conical solid-body target with viscous heating of deuterium.
    Additional Material: 12 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640100202
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  • 246
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    Eigensolution reanalysis of modified structures using perturbations and Rayleigh quotients (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 111-119 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new eigensolution reanalysis method for modified structures is developed and presented based on the usual first-order perturbation scheme and the Rayleigh quotients. By this method, the accuracies of the eigensolutions of the modified structures computed by perturbation methods are improved. A numerical example is presented and the accuracies of the usual first-order perturbation method, second-order perturbation method, William B. Bickford method and the proposed method are compared.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640100203
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  • 247
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    Perturbation method for computing eigenvalue bounds in structural vibration systems with interval parameters (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 121-134 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this study a perturbation method for computing the upper and lower bounds of eigenvalues of structural vibration systems with interval parameters is presented. The eigenproblem of the uncertain (interval) structure is expressed by equations consisting of the uncertainties. If the uncertainity is small in parameters, the eigensolutions of uncertain structures can be obtained efficiently by the perturbation method presented. A numerical example is given to demonstrate the validity of the method.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640100204
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  • 248
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    Accuracy and efficiency of multivariant finite elements for three-dimensional simulation of viscous incompressible flows (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 135-148 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The performance of the univariant finite element Q1P0 and the multivariant finite elements Q1+P0 and R2+P0 are compared for simulation of three-dimensional incompressible viscous flows. Incompressible flow vortices for the R2+P0 element are presented. For the two flows simulated, the R2+P0 element is found to be not only the most accurate but also computationally the most efficient of the three types of finite element used. For one of the two flows simulated, the pressure distribution obtained by using the Q1P0 element is found to be afflicted with the checker-board spurious pressure mode. For the uniform finite-element mesh used, the checker-board pressure mode is eliminated by taking a weighted average of the pressure over the neighbouring Q1P0 elements.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640100205
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  • 249
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    Conference diary (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 179-181 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640100209
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  • 250
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    Truncated envelope peconditioning technique (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 149-154 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the paper the use of a truncated envelope technique is discussed as a preconditioning for the conjugate gradient method for solving large linear systems of equations with symmetric positive-definite matrices. An algorithm to generate a truncated envelope is introduced. Computational experience with systems of linear equations from the Harwell-Boeing collection is presented to highlight the efficiency of this approach.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640100206
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  • 251
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    Addressing the corner problem in BEM solution of heat conduction problems (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 385-392 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical problem which features prominently in the implementation of the boundary-element method (BEM) for the solution of heat-conduction problems arises from double-valued heat fluxes at boundary corners. This problem is readily dealt with by explicitly treating nodal heat fluxes as double-valued prior to assembly of the nodal equations. This formulation is very flexible as it also permits imposing discontinuous thermal conditions at any boundary node. However, at corner nodes where temperature only is prescribed, the scheme leads to two unknowns, while only one nodal BEM equation is available there. An additional equation which closely follows the previous work of Walker and Fenner is derived for these nodes, and this provides sufficient information to resolve the upstream and downstream values of the heat flux at the temperature node. The additional equation is general, is free of heuristic constraints, and is applicable through the wide range of acute, shallow, obtuse and re-entrant angles encountered in practice. Numerical examples are used to compare the present method with the Walker and Fenner approach and with analytical solutions. Results indicate both improved accuracy and generality, thus validating the present method.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640100504
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    Efficient refinement/derefinement algorithm of nested meshes to solve evolution problems (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 403-412 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An adaptive refinement/derefinement algorithm of nested meshes is presented. Some definitions are introduced. The main properties of the derefinement algorithm are remarked upon and its efficiency is shown through two numerical examples: a time-dependent convection-diffusion problems with dominant convection and a quasistationary problem.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640100506
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    Announcements (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 425-426 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640100509
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    Masthead (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994) 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640100601
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    Effect of finite-element mesh topology on simulating mechanical breakdown in solids (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 413-420 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Fracture in heterogeous solids can be simulated with finite elements. We compare simulations of mechanical breakdown using meshes based on two types of geometrical elements: quadrilaterals and hexagons. The different co-ordination of the meshes leads to important differences in the load-carrying geometry close to failure. Hexagonal elements give a better representation of failure in brittle solids, whereas quadrilateral elements have a resemblance to fibrous solids.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640100507
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    Conference diary (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 497-499 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640100609
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    Critical look on new approach for geometrically evolving domains in geomechanics (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 469-480 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Numerical modelling of geometrically evolving domains, such as multistep construction, accretion and excavation, has always been of great interest to geotechnical engineers. Stress, strain and pore-pressure changes depend on hydromechanical properties and the loading process. Several techniques are proposed in the literature for numerical simulation of excavation or backfilling processes. These are mostly based on a natural methodology that consists in dividing the problem into several time steps, each coinciding with the addition or removal of one layer which is then modelled by means of several elements. Unfortunately, as in these methods the evolving parameters and their relative influence are not explicit, it is not possible to determine their accuracy. A more rigorous approach lies in the geometrical transformation of the studied domain, depending on the time variable for a reference domain in which the conservation equations are verified. The application of this methodology implies a great number of calculations. By using limited development techniques of the Jacobian of transformations it is possible to reduce the volume of computations. Such a technique results in approximations which can be evaluated.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640100606
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    Simplified heuristic Fourier analysis of iteration convergence rates (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 481-487 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Chan and Elman (1989) have recently shown that heuristic Fourier analysis can be used to determine approximate convergence rates of iterative methods. Here we present a simple procedure and useful relations that facilitate the practical application of this method. The procedure is based on the fact that the mesh spacing h is typically small, so that attention may be restricted to the asymptotic behaviour of the convergence rate R for small h. We accordingly derive simple expressions for the first few coefficients in a Taylor series expansion of R in powers of h. These coefficients are expressed in terms of derivatives with respect to h of the complex Fourier growth factor ξ rather than its modulus |ξ|. The required derivatives can then be obtained by implicit differentiation without explicitly solving for ξ, which further simplifies the analysis. The overall procedure is illustrated by applying it to the Jacobi, Gauss-Seidel and successive overrelaxation methods, for which we obtain results asymptotically equivalent to those of Chan and Elman. We also analyse the effect of second-order Richardson acceleration on the Jacobi method, for which we obtain an asymptotic convergence rate in precise agreement with classical analysis.
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    URL: http://dx.doi.org/10.1002/cnm.1640100607
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    A self-adaptive method for the GFDF solution of parabolic problems defined over 3D domains of general shape (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 531-543 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A self-adaptive method for the solution of elliptic and parabolic problems defined over 3D general multiconnected regions by generalized finite-difference formulae, with boundary approximation by means of polyhedra, is proposed. Different approaches to space refinements are studied and implemented. Numerical examples are given.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640100705
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    Numerical procedure for thermal creep stress in mass concrete structures (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 545-554 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the paper the experimental results considering the effects of temperature on the elastic modulus and creep of concrete are introduced into the mathematical models of the three-dimensional finite-element method to improve the calculation of creep stresses in mass concrete structures. The finite-element implementation of the exponential algorithm for concrete creep at variable temperatures is studied. The numerical solution procedure for thermal creep stresses in mass concrete structures with temperature effects is presented and a three-dimensional finite-element program is developed.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640100706
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    On the stabilization of the rectangular 4-node quadrilateral element (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 555-563 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The standard bilinear displacement field of the plane linear elastic rectangular 4-node quadrilateral element is enhanced by incompatible modes. The resulting gradient operators are separated into constant and linear parts corresponding to underintegration and stabilization of the element stiffness matrix. Minimization of potential energy is used to generate exact analytical expressions for the hourglass stabilization of the rectangle. The stabilized element is shown to coincide with the element obtained by the mixed assumed strain method.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640100707
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    Conference diary (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 577-579 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640100709
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    Announcements (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 580-582 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640100710
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    Empirical way to improve stress accuracy at stress concentrations in finite element analysis (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 565-576 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The nodal stresses in a finite element may be calculated in two ways: (a) directly at the nodes; (b) by bilinear extrapolation from the stresses at the 2 × 2 Gauss points. In both cases the von Mises stress is computed from the averaged nodal stresses. In areas of stress concentration, when the mesh is not adequately refined, there is a significant difference between the maximum von Mises stresses when methods (a) and (b) are used. By means of numerical examples it is shown that method (a) is superior to (b). Using both stress values an empirical formula, based on numerous FEM results, is presented for improving the accuracy of the maximum von Mises stress. The error reduction is considerable. Only plane stress problems with 8-node quadrilateral isoparametric elements are considered.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640100708
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    Masthead (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994) 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640100801
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    Stochastic boundary-element methods applied to 3D elastic problems and reliability of structural strength (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 583-589 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The stochastic boundary-element method (SBEM) is developed in this paper for 3D elastic problems and reliability analysis of structural components. The integral equations of BEM are derived partially by random variables, and the integral equations of SBEM are established. Considering the applied loads and the limitation of material strength to be a Gauss distribution, the numerical results in this paper show good agreement with those obtained from Monte Carlo simulation and theoretical solutions.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640100802
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    The unimportance of the spurious root of time integration algorithms for structural dynamics (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 591-597 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Most commonly used second-order-accurate, dissipative time integration algorithms for structural dynamics possess a spurious root. For an algorithm to be accurate, it has been suggested that the spurious root must be small and ideally be zero in the low-frequency limit. In the paper we show that good accuracy can be achieved even if the spurious root does not tend towards zero in the low-frequency limit. This permits more flexibility in the design of time integration algorithms. As an example, we present an algorithm that has greater accuracy than several other dissipative algorithms even though for all frequencies its spurious root is non-zero. We also show that the degraded performance of the Bazzi-ρ algorithm is not due to its non-zero spurious root.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640100803
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    Variational formulation for Timoshenko beam element by separation of deformation mode (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 599-610 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A variational formulation for a Timoshenko beam element is derived by the separation of the deformation mode into the bending deflection and shear deflection. Shear deflection is projected into bending deflection and the projection matrix is constructed by using the equilibrium equation and the relation of force and displacement. The exact stiffness matrix of the Timoshenko beam element can be obtained by the present method. Examples are solved in order to show the effectiveness of the beam element in comparison with other elements.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640100804
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    Optimal uniform finite difference schemes of order two for stiff initial value problems (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 611-622 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents finite difference schemes of order two for stiff initial-value problems, with a small parameter ε multiplying the first derivative. The schemes are a modified form of the classical trapezoidal rule. They are both optimal and uniform with respect to the small parameter ε, that is, the solution of the difference schemes satisfies error estimates of the form \documentclass{article}\pagestyle{empty}\begin{document}$$ \left|{u\left({t_i} \right) - u_i} \right| \le C\ min \left({h^2,\varepsilon} \right) $$\end{document} Where C is independent of i, h and ε. Here h is the mesh size and ti in any mesh point. The schemes presented in this paper are different from the scheme of order two avaiable in the literature. Finally, numerical experiments are presented.
    Additional Material: 5 Tab.
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    URL: http://dx.doi.org/10.1002/cnm.1640100805
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    An alternative approach for large deflection analysis of axisymmetric plates on elastic foundation (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 623-632 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The geometric non-linear behaviour of thin axisymmetric circular plates on an elastic foundation is studied in the paper by using a boundary integral equation approach. A plate analogue procedure is suggested to simplify the solution. With such simplification, the foundation reaction can be arbitrary functions of plate deflection, rotation and curvatures. The boundary integral equation of thin plates and the fundamental solution of a biharmonic equation are employed for both bending and plane stress analysis. A number of numerical examples are given in the paper to show the effectiveness of the proposed method.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640100806
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    A time-splitting finite difference method for two-dimensional diffusion with an integral condition (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 649-660 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new fourth-order locally one-dimensional (LOD) finite difference scheme based upon the Noye-Hayman method for one-dimensional diffusion is used to solve a two-dimensional time-dependent diffusion equation with an integral condition replacing one boundary condition. Numerical testing shows this gives better results than a locally one-dimensional scheme based on the classical forward-time centred-space (FTCS) method for one-dimensional diffusion except when the diffusion number is 1/6 and the methods are identical. Results from some numerical experiments are presented.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640100808
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    Conjugate gradient based projection: A new explicit computational methodology for frictional contact problems (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 633-648 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: With special attention towards the applicability to parallel computation or vectorization, a new and effective explicit computational approach for linear complementary formulations involving a conjugate gradient based projection methodology is proposed in this study for contact problems with Coulomb friction. The overall objectives are focused towards providing an explicit methodology of computation for the complete contact problem with friction. In this regard, the primary idea for solving the linear complementary formulations stems from an established search direction which is projected to a feasible region determined by the non-negative constraint condition; this direction is then applied to the Fletcher-Reeves conjugate gradient method resulting in a powerful explicit methodology which possesses high accuracy, excellent convergence characteristics, fast computational speed and is relatively simple to implement for contact problems involving Coulomb friction. Numerical test cases are also included to demonstrate the proposed methodology for contact problems with friction.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640100807
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    Non-linear finite element analysis of solids and structures, volume 1: Essentials, M. A. Crisfield, John Wiley. ISBN: 0-471-92956-5 (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 667-667 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640100810
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    Announcements (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 668-670 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640100811
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    On the large time behaviour of transient dynamic kernels for two-dimensional wave scattering (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 661-665 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An essential feature of the transient dynamic kernels for any time domain boundary integral equation is that they decay towards the static kernels for large time increments. The purpose of the paper is to show that the kernels of Mansur and Brebbia (1982), which are expressed in the form of generalized mathematical functions, do exhibit the correct decay property in contradiction to the claims of Israil and Banerjee (1990). Mansur and Brebbia express the fundamental solution wave discontinuity in terms of the generalized functions H(t) and δ(t), the Heaviside and Dirac delta functions, but do not explicitly demonstrate the required long time behaviour. In the 1990 paper the temporal discontinuity of the kernels is expressed by conventional functions in two time regimes and is shown to possess the correct long time behaviour, while it is claimed that the kernels in the 1982 paper do not. It is shown here that, assuming either constant or linear variation in time, usage of the generalized functions in the fundamental solution does yield the static fundamental solution for large time steps, as expected.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640100809
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    Conference diary (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 671-672 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640100812
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    Topology design with optimized, self-adaptive materials (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 1323-1350 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Significant performance improvements can be obtained if the topology of an elastic structure is allowed to vary in shape optimization problems. We study the optimal shape design of a two-dimensional elastic continuum for minimum compliance subject to a constraint on the total volume of material. The macroscopic version of this problem is not well-posed if no restrictions are placed on the structure topoiogy; relaxation of the optimization problem via quasiconvexification or homogenization methods is required. The effect of relaxation is to introduce a perforated microstructure that must be optimized simultaneously with the macroscopic distribution of material.A combined analytical-computational approach is proposed to solve the relaxed optimization problem. Both stress and displacement analysis methods are presented. Since rank-2 layered composites are known to achieve optimal energy bounds, we restrict the design space to this class of microstructures whose effective properties can easily be determined in explicit form. We develop a series of reduced problems by sequentially interchanging extremization operators and analytically optimizing the microstructural design fields. This results in optimization problems involving the distribution of an adaptive material that continuously optimizes its microstructure in response to the current state of stress or strain. A further reduced problem, involving only the response field, can be obtained in the stress-based approach, but the requisite interchange of extremization operators is not valid in the case of the displacement-based model.Finite element optimization procedures based on the reduced displacement formulation are developed and numerical solutions are presented. Care must be taken in selecting the discrete function spaces for the design density and displacement response, since the reduced problem is a two-field, mixed variational problem. An improper choice for the solution space leads to instabilities in the optimal design similar to those encountered in mixed formulations of the Stokes problem.
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    URL: http://dx.doi.org/10.1002/nme.1620370805
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    Numerical simulation of hydraulic jump (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 1381-1397 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Hydraulic jump on a straight horizontal channel with supercritical Froude numbers 2·0 and 4·0 is numerically simulated by solving the Reynolds averaged Navier-Stokes equations. Turbulence is modelled through the k-∊ closure equations and the mixed Eulerian-Lagrangian description of flow is utilized to overcome the problem posed by moving free boundary. Time stepping is done via fractional step method and pressure is determined from Poisson's equation. Galerkin finite element method with three-noded triangular elements is used for spatial discretization. A detailed study of the internal and external characteristics of hydraulic jump is done and compared with experimental values where possible. Surface roller and recirculation zone are found to play a dominant role in turbulence generation and dissipation.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620370807
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    Model reduction and process control of thermomechanical behaviour of non-linear material deformation (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 3135-3152 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes a design procedure for metal forming processes by using the controllable subspace of the full system. The velocity profile of the moving die is designed using the reduced order system. The metal forming processes are simulated using non-linear finite element methods based on the rigid viscoplastic flow formulation. The balanced model reduction technique is applied to reduce the full state space model to a reduced order model that retains the controllable subspace of the thermomechanical system. The linear quadratic regulator theory with output tracking is used as an off-line design tool to design the die velocity schedule. The process design is carried out to maintain the strain rate of the critical portion of the billet at a desired value. The procedure for designing the process parameters is demonstrated using two case studies.
    Additional Material: 12 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620371808
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    On the application of multi-step integration methods to infinitesimal elastoplasticity (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 3169-3184 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This article proposes an implicit algorithm for time integration of the differential/algebraic equations of small-deformation elastoplasticity in strain space. The algorithm employs a two-step backwards differentiation formula and a standard operator-split procedure. Second-order accuracy and non-linear stability are established under appropriate constitutive restrictions. The algorithm is implemented for the model of J2-plasticity and numerical simulations are conducted that illustrate its applicability and accuracy.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620371810
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    A finite element algorithm for elliptical equations over unstructured domains on a data parallel computerComputational resources were provided by Sandia National Laboratories, Albuquerque, New Mexico and Los Alamos National Laboratories, Los Alamos, New Mexico. (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 3153-3167 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the past, most finite element algorithms on data-parallel computers have been limited to structured problem domains. Here, we consider methods to generalize the finite element method on data-parallel architectures to unstructured domains. A nodal assembly algorithm is described which effectively allows for both the generation of the sparse interaction matrix (coefficient matrix) and its solution via a preconditioned conjugate-gradient type routine utilizing several polynomial preconditioners on the Connection Machine 200 (CM-200). Jacobi preconditioning along with Neumann series and least-squares polynomial preconditioners are presented and implemented are presented and implemented. Only the Jacobi preconditioner produces an improvement in the convergence time for the problems examined. Several irregular interprocessor communication protocols available on the CM-200 are investigated in the solution portion of the algorithm, yielding differing performance characteristics. For one such protocol, sustained performance of over two-hundred MFlops/s, is demonstrated for a test problem on a 512 processing element CM-200 in slicewise mode. The results are discussed and conclusions are drawn concerning this finite element algorithm.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620371809
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    Adaptive control system using the fuzzy theory for transient multi-dimensional thermohydraulics calculations (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 3397-3415 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An adaptive control system to yield optimum time step sizes was developed using the fuzzy theory for transient single-phase multi-dimensional thermohydraulic calculations. Applications of the control system revealed a considerable amount of the computing time savings, typically by 50-75 per cent of the computing time required when the time step size was not controlled by the system. The result obtained in this work is very encouraging in the sense that the adaptive control system would be used as one of the efficient measures to save computing efforts when one wishes to perform extremely large scale computations in transient thermohydraulics.
    Additional Material: 26 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620372002
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    Enhanced superconvergent patch recovery incorporating equilibrium and boundary conditions (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 3417-3440 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Patch recovery based on superconvergent derivatives and equilibrium (SPRE), an enhancement of the Superconvergent Patch Recovery (SPR), is studied for linear elasticity problems. The paper also presents a further improvement for recovery of derivatives near boundaries, SPREB, where either tractions or displacements are prescribed. This is made by inclusion of weighted residual errors at boundary points in the patch recovery. A pronounced improvement in the post processed gradients of the finite element solution is observed by this method.
    Additional Material: 19 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620372003
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    A temperature-based formulation for finite element analysis of generalized phase-change problems (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 3441-3465 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element formulation for solving multidimensional phase-change problems is presented. The formulation considers the temperature as the unique state variable, it is conservative in the weak form sense and it preserves the moving interface condition. In this work, an approximate jacobian matrix that preserves numerical convergence and stability is also derived. Furthermore, a comparative analysis with other different phase-change finite element techniques is performed. Finally, several numerical examples are analysed in order to show the performance of the proposed methodology.
    Additional Material: 24 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620372004
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    A numerical method for introducing an arbitrary yield function into rigid-viscoplastic FEM programs (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 3467-3487 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Many standard yield functions (Hill, von Mises, etc,…) allow the derivation of simple equations relating the effective strain rate to principal strain rates explicitly. Such yield functions are easily implemented in rigid-viscoplastic finite element method programs. Other yield functions (Hosford, e.g.) do not allow for this simple approach. A numerical method was proposed in this paper to solve this problem which meets the requirement of rigid-viscoplastic finite elements and can generate the material stiffness terms (first and second derivatives of the effective strain rate with respect to principal strain rates) at any strain state. The numerical method was found to be numerically efficient, accurate and robust. As an example of the procedure, Hosford's yield function was introduced in a rigid-viscoplastic finite element program and results for the punch stretching simulation were compared with Hill-type materials. The numerical efficiency of the method was also compared. Simulation of full dome formability test, plane strain and square punch stretching was performed by this numerical method with Hosford's yield function.
    Additional Material: 17 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620372005
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    Isoparametric Hermite elements (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 3489-3519 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Isoparametric Hermite elements are created using Bogner-Fox-Schmit rectangles on a reference domain and mapping these numerically onto the computational domain. The difficulties involved in devising explicit C1 shape functions for isoparametric elements are thus avoided, and the resulting elements have all the benefits of full C1 continuity, the simplicity of the Bogner-Fox-Schmit element and the geometrical flexibility expected from higher-order isoparametric elements. The numerical mapping consists in the finite element solution of a linear boundary value problem, which is inexpensive and is carried out as a preprocessing operation - the required derivatives of the mapping then being supplied to the main analysis as data. Some care is required in defining the differential boundary conditions, and guidance on this is provided. Examples are given showing the success of the mapping procedure, and the use of the resulting elements in the solution of some boundary value problems. The numerical results confirm a convergence analysis provided for the new isoparametric Hermite element.
    Additional Material: 19 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620372006
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    Dynamic condensation: The ‘Free Mode’ method (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 3521-3543 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The dynamic condensation methods make it possible to reduce the size of large matrix systems occurring in mechanics in order to obtain an accurate description of behaviours. In the first instance, we have reviewed the methods currently available. Then, we have presented the latest improvements which have been introduced with respect to the ‘Free Mode’ method. The use of an innovative technique for the determination of residual flexibility matrices, the consideration of an additional term in the expansions and a shift in frequencies have made this method particularly accurate and worthy of interest. In the present paper, we have presented an example which, however simple, has the merit of highlighting the qualities of the proposed method by drawing comparisons with the results achieved through the application of other methods.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620372007
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  • 288
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    Announcements (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 3581-3582 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620372010
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    Conference diary (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 3583-3584 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620372011
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  • 290
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    Ray tracing with a space-filling finite element mesh (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 3571-3580 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new ray-tracing technique is presented which does not work with ray-object intersections per se, but is based on the traversal of an unstructured tetrahedral mesh providing a convex enclosure of a scene of polyhedral objects. The tetrahedral mesh provides tight bounding and an adaptive subdivision of space. This non-hierarchical data structure is traversed adaptively until one is led directly and unconditionally to the first object intersected. Rendering times are directly related to the average thickness of the enclosing mesh since all tetrahedra are traversed in constant time.Since the proposed algorithm operates directly with volume elements, it allows for volumetric rendering effects. Volume rendering or anisotropic media can be implemented without any further effort. This is an important advantage as compared to usual techniques, which only operate on surface data.Timings for several examples show that the use of this type of ray-tracing technique, which is more suitable for general purpose visualization codes than traditional techniques, results in CPU times that are comparable with the best ray-tracing techniques presently used. This is an unexpected and important result, as the vectorization and parallclization of the proposed technique are straightforward, in contrast with traditional ray-tracing techniques.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620372009
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  • 291
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    A space-time coupled p-version least-squares finite element formulation for unsteady fluid dynamics problems (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 3545-3569 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a p-version least-squares finite element formulation for unsteady fluid dynamics problems where the effects of space and time are coupled. The dimensionless form of the differential equations describing the problem are first cast into a set of first-order differential equations by introducing auxiliary variables. This permits the use of C° element approximation. The element properties are derived by utilizing p-version approximation functions in both space and time and then minimizing the error functional given by the space-time integral of the sum of squares of the errors resulting from the set of first-order differential equations. This results in a true space-time coupled least-squares minimization procedure.A time marching procedure is developed in which the solution for the current time step provides the initial conditions for the next time step. The space-time coupled p-version approximation functions provide the ability to control truncation error which, in turn, permits very large time steps. What literally requires hundreds of time steps in uncoupled conventional time marching procedures can be accomplished in a single time step using the present space-time coupled approach. For non-linear problems the non-linear algebraic equations resulting from the least-squares process are solved using Newton's method with a line search. This procedure results in a symmetric Hessian matrix. Equilibrium iterations are carried out for each time step until the error functional and each component of the gradient of the error functional with respect to nodal degrees of freedom are below a certain prespecified tolerance.The generality, success and superiority of the present formulation procedure is demonstrated by presenting specific formulations and examples for the advection-diffusion and Burgers equations. The results are compared with the analytical solutions and those reported in the literature. The formulation presented here is ideally suited for space-time adaptive procedures. The element error functional values provide a mechanism for adaptive h, p or hp refinements. The work presented in this paper provides the basis for the extension of the space-time coupled least-squares minimization concept to two- and three-dimensional unsteady fluid flow.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620372008
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    Masthead (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994) 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620372101
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    The advancing-front mesh generation method revisited (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 3605-3619 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a mesh generation method of the advancing-front type which is designed in such a way that the well-known difficulties of the classical advancing-front method are not present. The retained solution consists of using the first steps of a Voronoï-Delaunay method to construct a background mesh which is then used to govern the algorithm. The two-dimensional case is considered in detail and possible extensions to adaption problems and three dimensions are indicated.
    Additional Material: 17 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620372103
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  • 294
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    A postprocessed error estimate and an adaptive procedure for the semidiscrete finite element method in dynamic analysis (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 3585-3603 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the paper we present a postprocessed type of a posteriori error estimate and a h-version adaptive procedure for the semidiscrete finite element method in dynamic analysis. In space the super-convergent patch recovery technique is used for determining higher-order accurate stresses and, thus, a spatial error estimate. In time a postprocessing technique is developed for obtaining a local error estimate for one step time integration schemes (the HHT-α method). Coupling the error estimate with a mesh generator, a h-version adaptive finite element procedure is presented for two-dimensional dynamic analysis. It updates the spatial mesh and time step automatically so that the discretization errors are controlled within specified tolerances. Numerical studies on different problems are presented for demonstrating the performances of the proposed adaptive procedure.
    Additional Material: 19 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620372102
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    Transient analysis of tube rolling processes by a semi-analytical formulation (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 3621-3632 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A semi-analytical formulation is presented for transient metal-forming processes which, being axisymmetric in geometry, are subjected to non-axisymmetric loads and boundary conditions. The problems are described in terms of the flow formulation, and the pseudo-concentration method (two material based) is used to account for time integration and non-axisymmetric free surfaces. Proper Fourier series expansion of both the scalar fields defined to identify the free surfaces and of all the variables of the mechanical problem allows the performance of an advective transport-corresponding to time integration-for a non-axisymmetric velocity field. A block diagonal matrix is obtained for each harmonic component, as it has been achieved for the constant time solution. The new configuration found as a result of this analysis is taken to calculate the velocity field for the incremented time, which in turn is used to perform the following time step.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620372104
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    Inelastic post-buckling analysis of truss structures by dynamic relaxation method (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 3633-3657 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents the inelastic post-buckling analysis of truss structures by the Dynamic Relaxation (DR) method. A simplified inelastic finite element formulation for truss element and new algorithms are proposed for Elastic Post-Buckling (EPB) analysis and Inelastic Post-Buckling (IEPB) analysis using the DR method. The post-buckling paths for elastic, EPB and IEPB analyses are completely traced using the variable-arc-length method. Four numerical examples are presented to illustrate the application of the proposed algorithms.
    Additional Material: 27 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620372105
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  • 297
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    Stress resultant geometrically non-linear shell theory with drilling rotations. Part III: Linearized kinematics (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 3659-3683 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A consistent formulation of the geometrically linear shell theory with drilling rotations is obtained by the consistent linearization of the geometrically non-linear shell theory considered in Parts I and II of this work. It was also shown that the same formulation can be recovered by linearizing the governing variational principle for the three-dimensional geometrically non-linear continuum with independent rotation field. In the finite element implementation of the presented shell theory, relying on the modified method of incompatible modes, we were able to construct a four-node shell element which delivers a very high-level performance. In order to simplify finite element implementation, a shallow reference configuration is assumed over each shell finite element. This approach does not impair the element performance for the present four-node element. The results obtained herein match those obtained with the state-of-the-art implementations based on the classical shell theory, over the complete set of standard benchmark problems.
    Additional Material: 17 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620372106
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    Incompressibility and axisymmetry: A modified mixed and penalty formulation (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 1623-1649 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes a modified penalty and two-field mixed formulation for the analysis of incompressible axisymmetric field problems, A discussion of the existing difficulties with incompressibility and axisymmetric formulations is covered in detail. To facilitate the exact satisfaction of incompressibility in axisymmetric bodies during finite element modelling procedures, a modified shape function is used in the description of radial displacement. Further, the modification to the radial displacement interpolation function overcomes the lacunae of the existing mixed and penalty formulations by eliminating the bias of the isoparametric element behaviour in a divergence free continuum state. A six-noded triangular element, with a central bubble function, is considered to amplify the issues connected with incompressibility in axisymmetric geometries. The bilinear displacements, along with three reduced/selective integration rules in the case of the modified penalty method and three discontinuous pressure nodes in the element for the case of the modified mixed method, are shown to be equivalent in the case of a numerical study of the incompressible cylinder expansion problem. The displacements, stresses and pressure values obtained from the modified methods will be shown to be in close agreement with exact solutions available from the literature. The numerical treatment proposed in the present study clearly demonstrates the performance and the need for modified methods in the analysis of incompressible axisymmetric engineering problems.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620371002
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  • 299
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    Preconditioned Krylov solvers for BEA (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 1651-1672 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The performance of a number of preconditioned Krylov methods is analysed for a large variety of boundary element formulations. Low- and high-order element, two-dimensional (2-D) and three-dimensional 3-D, regular, singular and hypersingular, collocation and symmetric Galerkin, single- and multi-zone, thermal and elastic, continuous and discontinuous boundary formulations with and without condensation are considered. Preconditioned Conjugate Gradient (CG) solvers in standard form and a form effectively operating on the normal equations (CGN), Generalized Minimal Residual (GMRES), Conjugate Gradient Squared (CGS) and Stabilized Bi-conjugate Gradient (Bi-CGSTAB) Krylov solvers are employed in this study. Both the primitive and preconditioned matrix operators are depicted graphically to illustrate the relative amenability of the alternative formulations to solution via Kryiov methods, and to contrast and explain their computational performances. A notable difference between 2-D and 3-D BEA operators is readily visualized in this manner. Numerical examples are presented and the relative conditioning of the various discrete BEA operators is reflected in the performance of the Krylov equation solvers. A preconditioning scheme which was found to be uncompetitive in the collocation BEA context is shown to make iterative solution of symmetric Galerkin BEA problems more economical than employing direct solution techniques. We conclude that the preconditioned Krylov techniques are competitive with or superior to direct methods in a wide range of boundary formulated problems, and that their performance can be partially correlated with certain problem characteristics.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620371003
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    The variational formulation and solution of problems of finite-strain elastoplasticity based on the use of a dissipation function (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 1673-1695 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The solution of initial-boundary value problems involving finite elastoplastic deformations is discussed. The formulation considered differs from conventional formulations in that the evolution law is expressed in terms of the dissipation function. A generalized midpoint rule is used to obtain an incremental problem, a variational form of which is derived. The finite element method is used for spatial discretization, and an algorithm to solve the resulting discrete problem is developed. This algorithm has the predictor-corrector structure common to most solution procedures for problems in plasticity. Methods for imposing the plastic incompressibility constraint are investigated. Solutions to two axisymmetric examples obtained using the proposed algorithm are presented and compared with those obtained by other authors.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620371004
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