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  • 201
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 59 (1996), S. 7-14 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In this article, an attempt was made to develop an activation process model. The average energy of the translational motion of the atoms, taking part in the elementary activation process and being in the thermodynamic equilibrium with thermal radiation, was obtained using the quantum canonical Gibbs distribution and the model principles of elementary activation. The degeneracy and exclusion of some excited vibrational levels were taken into consideration, the result being a strong dependence of the probability of surmounting the activation barrier on the behavior of the excited vibrational states of the quantum subsystems. As an application of the development model, the formulas of the preexponential factor for solid-state atomic diffusivity and first-order chemical reaction rate constants were derived. Quantitative analysis of the atomic diffusion in solids in the framework of our model has made it possible to describe the diffusion processes in metals, covalent semiconductors, as well as diffusion anomalies, connected with the “nonclassical” behavior of the empirical Arrhenius dependence. A possible physical essence of a kinetic compensation effect is discussed. It was shown that compensation may be caused by only changing the degeneracy of the vibrational levels of the quantum subsystems. © 1996 John Wiley & Sons, Inc.
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  • 202
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Nonlocal density functional calculations and a semiempirical modified Born method for computing free energies of hydration were used to calculate the electrode potentials for a series of nitroimidazoles to a mean accuracy of about 80 mV. The density functional calculations used the nonlocal Becke '88 functional for exchange and either the nonlocal Lee-Yang-Parr or the local Vosko-Wilk-Nusair functionals for correlation and were performed at the HF/3-21G geometry. The most suitable geometry for these calculations was determined from a survey of various semiempirical, Hartree-Fock (HF) and density functional methods, with a variety of basis sets. The HF/3-21G method was found to yield a very favorable compromise between speed and accuracy in the determination of the geometry of 2-nitroimidazole, but the small basis set density functional calculations performed very badly. Density functional atom-optimized basis sets were found to give better overall results than traditional Pople-type basis sets. The free energy of hydration calculations employed the AM1 SM2 method. Both the gas-phase energies and the free energies of hydration made a significant contribution to the computed electrode potential. Indeed, an inverse relationship was found between the gas-phase electron affinity and the difference in free energy of hydration between the neutral nitroimidazole and its radical anion. The protocol established here may be useful for investigating novel bioreductive agents. © 1996 John Wiley & Sons, Inc.
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  • 203
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 59 (1996), S. 167-172 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Molecular orbital calculations are reported on the structure and electronic properties of both 2-nitrophenylcyanate and 2-nitrophenylthiocyanate using both the semiempirical AM1 and PM3 methods and the ab initio 3-21G and 6-31G** basis sets. The resulting structures are compared with crystallographic data where available. The marked difference in biological activity observed between the two molecules appears to be attributable to large differences in their electronic properties rather than to any geometric factors. © 1996 John Wiley & Sons, Inc.
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  • 204
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Theoretical calculations of the potential energy surface (PES) for the [NH3 + HCl] system are presented using several standard ab initio methods such as Hartree-Fock (HF), second-order Møller-Plesset perturbation theory (MP2), coupled cluster (CC), complete active space self-consistent-field (CASSCF), density functional theory (DFT), and less traditional ab initio approaches such as Dirac-Fock four-components and the use of effective Hamiltonian techniques, such as the recently proposed K functional. All calculations predict a single minimum for the complex, corresponding to a hydrogen-bonded structure, confirming early studies. The dynamical and nondynamical contributions to the correlation energy are discussed for different cuts of the PES, involving different N(SINGLE BOND)Cl distances. The complex has also been characterized by performing a full geometry optimization within the HF and DFT schemes; with the latter we have performed also the vibrational analysis. The predicted binding energies and infrared (IR) spectrum are compared with other theoretical and experimental results. For the gas phase, we propose a binding energy of -5.3 ± 0.5 kcal/mol, thus revising the experimental value of -8.0 ± 2.8 kcal/mol; for the minimum, the predicted N(SINGLE BOND)H and H(SINGLE BOND)Cl distances are 5.91 ± 0.05 and 2.46 ± 0.05 a.u., respectively. When the computation is done with approximate inclusion of solvent effects (Onsager reaction field), the minimum is shifted and it corresponds to the ion pair NH+4·Cl- structure, similar to Mulliken's outer complex. Since the first ab initio computation for the NH4Cl complex is the pioneer work in 1967 by E. Clementi, the present work provides us with an opportunity to comment on some aspects of the evolution in computational chemistry, particularly for energy determinations. We have concluded our comments with the invitation to use four-components Fock-Dirac for molecules both with high and low Z atoms, rather than the traditional Hartree-Fock and related methods. In other words, we are of the opinion that the time is ready in quantum chemistry to switch from the Schrödinger to the Dirac representation, due to new developments in computer hardware and software. In addition, the use of effective Hamiltonians, like the recently proposed “K functional,” seems to deserve attention, because of their computational simplicity and physical reliability in predicting correlation corrections. © 1996 John Wiley & Sons, Inc.
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  • 205
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    International Journal of Quantum Chemistry 59 (1996), S. 379-390 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In a novel approach to molecular shape representation, molecular electronic density functions are treated as 3D hypersurfaces in a 4D Euclidean space, spanned by the three spatial coordinates and an electronic density threshold variable. The general objects resulting from this approach are topological spheres with handles, modeling the electron density. Based on this model, a new, simple representation of molecular topology of electron density is proposed, using a tree describing the evolution of topological spheres with handles as function of a varying density threshold. The vertices of the tree are characterized by nonnegative integers (the genea of the topological objects). This representation is compared to earlier, detailed 3D topological descriptions of molecular shape as well as to the more conventional molecular network (bond skeleton) representation. A variety of relevant topological equivalence relations of molecules are discussed and a new, global, molecular similarity measure is proposed. © 1996 John Wiley & Sons, Inc.
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  • 206
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    International Journal of Quantum Chemistry 59 (1996), S. 349-378 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An ab initio procedure for the calculation of atomic and molecular electronic wave functions, the Optimized-Basis-Set Multi-Configuration Spin-Coupled (OBS-MCSC) method, is generalized by introducing a separate linear combination of spin functions for each configuration, turning it into the OBS-GMCSC method. The ability to use a second-order minimization procedure in the computation of the wave function is maintained through appropriate generalization of the analytic expressions for the first and second derivatives of the energy with respect to the optimization parameters, as is the optional inclusion among the latter of the basis-function exponential parameters. The generalization, a variational improvement of the wave function, strengthens the connection with classical VB theory, of which the method can now be considered an optimized-orbitals variant, while maintaining the link with single-configuration Spin-Coupled theory, of which it may still be considered a multiconfiguration extension. The method can also be viewed as a nonorthogonal variant of the MCSCF approach. To demonstrate its practical feasibility and usefulness, the OBS-GMCSC method is applied to a study of the electronic structure and electron affinity of boron. © 1996 John Wiley & Sons, Inc.
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  • 207
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    International Journal of Quantum Chemistry 59 (1996), S. 503-503 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 208
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    International Journal of Quantum Chemistry 59 (1996), S. 495-501 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Two ab initio (ROHF and MP2), one local (SVWN), four hybrid (BHandH, BHandHLYP, Becke3LYP, and Becke3P86), and two nonlocal (BLYP and BP86) density functional theory (DFT) methods are used for calculating the dissociation energies of molecules that contain H(SINGLE BOND)O, O(SINGLE BOND)O and O(SINGLE BOND)C bonds. The sensitivity to the basis set of the prediction of bond dissociation energies with DFT methods was tested with Becke3LYP on the H(SINGLE BOND)O dissociation energy of water. The 6-31 + G(d) methods are chosen as the smallest basis set which produces reasonable results. The calculated values for all other ab initio and DFT methods were performed with these basis sets and then compared with the experimental data. The suitability of DFT methods for computing reliable bond dissociation energies of oxygen containing molecules is discussed. © 1996 John Wiley & Sons, Inc.
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  • 209
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    International Journal of Quantum Chemistry 59 (1996), S. 505-505 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 210
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    International Journal of Quantum Chemistry 60 (1996), S. 131-139 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In this study the work performed at our laboratory is outlined by emphasizing the leading role that the idea of average has in our research. © 1996 John Wiley & Sons, Inc.
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  • 211
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    International Journal of Quantum Chemistry 60 (1996), S. 141-146 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A quantitative reference for comparing molecules (and sites of molecules) likely to exchange electrons with a molecular or crystalline partner can be obtained by coupling such molecules to a model electron reservoir with a continuous energy spectrum. In this study the required procedure is defined and mathematically formulated, within the standard orbital scheme. The reservoir is modeled as an infinite linear chain of atoms with one atomic orbital whose coupling is larger than the largest half-bandwidth of the molecules to be compared, coupled by a suitable bond parameter to a specific site of the molecule. The resulting level broadening and local density of states (DOS) are determined using Dyson's equation to get a tractable expansion of the Green function of the molecule-reservoir system. An example of application and a brief discussion of the dependence of the results on the type of Hamiltonian utilized are given. © 1996 John Wiley & Sons, Inc.
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  • 212
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    International Journal of Quantum Chemistry 60 (1996), S. 147-156 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A technique for the configuration interaction (CI) study of many-electron systems is developed based on Rumer spin-coupling scheme for the antisymmetrized configuration state functions (CSF). Incorporating a new graphical approach, the primitive configurations have been generated in blocks of definite ionocities to permit ready association of possible spin functions with each of the primitive configurations. Simple as well as extended Hubard model Hamiltonians have been studied to test the efficiency of the method. Procedures have been incorporated to calculate various correlation functions using the spin-adapted CSFs without invoking explicit expansions in terms of slater determinants. © 1996 John Wiley & Sons, Inc.
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  • 213
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    International Journal of Quantum Chemistry 60 (1996), S. 167-171 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Multireference perturbation theory is examined in connection with the two partitions in the Møller - Plesset and Epstein - Nesbet schemes. The implementation of an efficient diagrammatic technique is described and two examples of application (diazene and the Cr2 molecule), involving large variational spaces, are provided. © 1996 John Wiley & Sons, Inc.
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  • 214
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    International Journal of Quantum Chemistry 60 (1996), S. 173-183 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A method of performing ab initio calculations of the electronic structure of fragments within a larger molecule is reported. The method uses the self-consistent group formalism of McWeeny together with the systematic use of a hybrid atomic orbital basis. The mutual compatibility of these two ideas is stressed and results are given for model calculations on fragments in saturated hydrocarbon chains and rings. © 1996 John Wiley & Sons, Inc.
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  • 215
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    International Journal of Quantum Chemistry 60 (1996), S. 157-166 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The Roothaan equations have been modified to compute molecular interactions between weakly bonded systems at the SCF level of theory without the basis set superposition error (BSSE). The increase in complication with respect to the usual SCF algorithm is negligible. Calculation of the SCF energy on large systems, such as nucleic acid pairs, does not pose any computational problem. At the same time, it is shown that a modest change in basis-set quality from 3-21G to 6-31G changes the binding energy by about 50% when computed according to standard SCF “supermolecule” techniques, while remaining practically constant when computed without introducing BSSE. Bader analysis shows that the amount of charge transferred between the interacting units is of the same order of magnitude when performed on standard SCF wave functions and those computed using the new method. The large difference between the corresponding computed energies is thus ascribed to the BSSE. © 1996 John Wiley & Sons, Inc.
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  • 216
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    International Journal of Quantum Chemistry 60 (1996), S. 213-224 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Formulas are derived for the density matrices belonging to an n-particle wave function built on the basis of single-center explicitly correlated Gaussian basis functions. An explicit formula for the first-order density matrix, P(r1, r′1), is obtained for computing the probability distribution P(r1, r1). Other formulas are derived for matrix elements of the first-order density operator P on a basis of single-particle Gaussian orbitals so that natural orbitals (NOs) can be expressed in such a basis. The method is illustrated for the case of the ground state of the helium atom using the 16-term (geminal) wave function by Singer and Longstaff (E = -2.90233 au) and a set of even-tempered Gaussian orbitals. The resulting natural orbitals compare favorably with natural orbitals from Cl expansions. The method is also applied to our 20 term (trimal) wave function for the ground state of dipositronium (E = -0.51560 au). Analysis is made in this case for pair correlation functions of both the electron-electron and the positron-electron pairs; results include the radial distributions of these pairs and their relative angular momentum. © 1996 John Wiley & Sons, Inc.
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  • 217
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    International Journal of Quantum Chemistry 60 (1996), S. 1165-1178 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We examine the state of the art of the solvation procedure called the polarizable continuum model (PCM), focusing our attention on the basic properties: energy of the solute, solvation energy, and their derivatives with respect to nuclear coordinates. The PCM method is based on the use of an effective solute Hamiltonian, where the solute-solvent potential is described in terms of continuous response functions with boundary conditions given in terms of the solute cavity surface. This exposition is mainly based on recent progress, a large part of which is still in press. The new procedures are quite effective, at the ab initio quantum mechanical level, but cannot be applied to very large solutes for the limitations of computer hardware. We introduce then other methods, presented here for the first time, which make possible the classical calculation of the solvation energy also for very large solutes (a few thousand atoms). The strategy outlined here regards a new method to define cavity surfaces (supplemented with analytical definitions of its partition in tesserae) and of their derivatives, combined with a fast noniterative method to compute solvation energy. Finally, we discuss the introduction of this procedure in hybrid quantum mechanical/molecular mechanics descriptions of large solutes (enzymes), where the quantum description is limited to the reacting portion of the enzyme. © 1996 John Wiley & Sons, Inc.
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  • 218
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    International Journal of Quantum Chemistry 60 (1996), S. 1249-1256 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Avoided crossing diagram parameters for the radical exchange reaction and the concerted exchange of two and three bonds are computed by using the approximated valence bond method, which is a nonorthogonal configuration interaction (CI) semiempirical method among the valence bond configuration functions. Here, each valence bond configuration function is a spin-adapted combination of Slater determinants constructed from the Heitler-London or Coulson-Fischer hybrid orbitals. Atomic orbitals integrals are evaluated using semiempirical philosophy, and these provide considerable saving of computer time compared with the most standard ab initio multistructure valence bond methods. The results indicate that the approximate valence bond method is capable of yielding reasonable results for the avoided crossing diagram parameters. These results also indicate that the diagram gap (G) is the decisive factor for the stability of symmetric clusters, Xn, although no clear correlation between the gap G and the geometric distortion is found for different values of n. © 1996 John Wiley & Sons, Inc.
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  • 219
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    International Journal of Quantum Chemistry 60 (1996), S. 1271-1277 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A practical procedure (FUERZA) to obtain internal force constants from Cartesian second derivatives (Hessians) is presented and discussed. It allows a systematic analysis of pair atomic interactions in a molecular system, and it is fully invariant to the choice of internal coordinates of the molecule. Force constants for bonds or for any pair of atoms in general are defined by means of the eigenanalysis of their pair interaction matrix. Force constants for the angles are obtained from their corresponding two-pair interaction matrices of the two bonds or distances forming the angle, and the dihedral force constants are similarly obtained using their corresponding three-pair interaction matrices. © 1996 John Wiley & Sons, Inc.
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  • 220
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    International Journal of Quantum Chemistry 60 (1996), S. 1291-1301 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We present a computational scheme to study the dynamics of many-electrons in molecular systems by wavepackets method. Several approaches to calculation of nonlinear optical properties for molecules under time-independent or time-dependent external electric fields are presented. Some simple examples of one-dimensional two- or three-electron systems are demonstrated concretely. Implications of these results are discussed in relation to the validity of the many electron wavepackets (MEWP) method. © 1996 John Wiley & Sons, Inc.
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  • 221
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    International Journal of Quantum Chemistry 60 (1996), S. 1303-1310 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A stochastic path-integral (SPI) technique for chemical reaction dynamics is explored. It is shown that this technique enables the direct computation of the transition amplitude with a finite space-time range, by generating a set of classical paths subject to simultaneous stochastic differential equations. The numerical values of the Boltzmann matrix elements for a harmonic potential are in good agreement with the analytical ones. Within the quantum transition state theory, the flux-flux autocorrelation function is also evaluated at 630 K for the H + H2 exchange reaction and is found to give a satisfactory agreement with the previous studies. To appraise the influence of the dimensionality, both one-dimensional Eckart potential and a full three-dimensional (3D) Liu-Siegbahn-Truhlar-Horowitz (LSTH) potential calculations have been performed. The calculated values of the Boltzmann matrix elements for the colinear and the full 3D cases are found to deviate slightly from each other in the lower temperature range. The 3D thermal rate constant is in very good agreement with the previous one. © 1996 John Wiley & Sons, Inc.
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  • 222
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    International Journal of Quantum Chemistry 60 (1996), S. 1403-1407 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In density functional theory (DFT) the exchange-correlation energy has to be approximated. One of the most widely used approximations to the correlation component, the Lee(SINGLEBOND)Yang(SINGLEBOND)Parr (LYP) functional does not obey nonuniform scaling requirements. We propose a modifying function that makes this functional satisfy nonuniform scaling constraints. As a result, two modified LYP functionals are suggested. One of them, optimized in a preliminary way, exhibits some properties better than the original LYP functional. This implies that nonuniform scaling requirements convey very important information and all approximate functionals in DFT should be made to satisfy these requirements. Our modifying factor could be used to improve the nonuniform scaling properties not only of Ec LYP [n] but also of most functionals which do not obey these conditions. © 1996 John Wiley & Sons, Inc.
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  • 223
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    International Journal of Quantum Chemistry 60 (1996), S. 1457-1468 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The Kohn-Sham eigenvalues were formally introduced into density functional theory as Lagrange multipliers in the implementation of the minimum principle for the total energy of a many-electron system. No general results are available concerning the physical significance of these one-electron eigenvalues (with the exception of the highest occupied level, which equals the Fermi energy). Recent ab initio calculations of dynamical response in metals make explicit use of the Kohn-Sham band structure, and associated wave functions, through the use of spectral representations. This opens up the possibility of examining the significance of the eigenvalues at an “empirical” level, i.e., through direct comparison with the results of spectroscopic measurements. A particularly interesting example is afforded by new inelastic x-ray scattering experiments on A1. For a special wave vector transfer, qo ≈ 1.5kF, the measured spectrum provides a direct mapping of the Kohn-Sham noninteracting spectrum. For a range of wave vectors about qo, the bare Kohn-Sham spectrum still reproduces all the main features of the measurements; this suggests that, in this metal, the Kohn-Sham eigenvalues are good approximations to the quasiparticle energies. We also discuss the interplay between Kohn-Sham bands and the energy of the “anomalous” plasmon in Cs, whose dispersion bears a signature of the excited-state band structure. Finally, and in a more formal framework, we outline the results of a first-principles comparison between quasiparticle amplitudes and Kohn-Sham wave functions at a jellium surface; the latter turn out to be excellent approximations to the former. © 1996 John Wiley & Sons, Inc.
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  • 224
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    International Journal of Quantum Chemistry 60 (1996), S. 1487-1497 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Minimal basis-set (STO-3G) direct and Fourier space restricted Hartree-Fock (RHF) calculations on the infinite regular (metallic) and alternating chains of lithium molecules, (-Li2-)x, are reported to illustrate two advantages of the Fourier representation method: accurate calculation of all lattice summations and faithful reproduction of the genuine features of the RHF approach for metallic cases. © 1996 John Wiley & Sons, Inc.
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  • 225
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    International Journal of Quantum Chemistry 60 (1996), S. 1505-1514 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The dependence of X-ray photoionization spectra on structural characteristics is assessed by one-particle Green's function calculations on the nearly isomeric adamantane, 1,4-dimethyl bicyclo [2,2,2] octane and 1,1,4,4-tetramethyl cyclohexane compounds. These calculations are carried out using the quasi-particle approximation and the diagonal 2ph-TDA renormalization scheme for the self-energy. The simulated spectra fingerprint remarkably the atomic connectivity from their inner valence part, through the interplay of energy degeneracies and the influence of torsional strains on electron binding energies. The boundary region between the inner and outer valence bands provides also specific signatures for molecular characteristics pertaining to conformational questions, namely the enforced conversion from the chair to the boat form of the cyclohexane units generating these compounds. © 1996 John Wiley & Sons, Inc.
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    International Journal of Quantum Chemistry 60 (1996), S. 1525-1536 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The local self-consistent field (LSCF) method which allows full SCF computations on a fragment of very long molecular systems represented by a classical force field has been adapted to the description of nonmetallic crystals. The periodicity of the network is achieved by modifying self-consistently the basic parameters of the classical subsystem (charges, geometric parameters) along the SCF iterative scheme. The method is tested on α-cristobalite. The parametrization of the quantum classical junction, achieved by localized bond orbitals has been performed with the help of a fragment located in the bulk. The stability of the method with respect to the size of the fragment and the size of the crystalline sample appears to be very good. The properties of fully hydroxylated (010) surface are corrected described. Modeling of water adsorption on the ideal surface as well as on two kinds of surface defects gives rise to very reasonable results with an absorption energies of ca 10 kcal/mol which are close to the upper limit of the experimental data. This preliminary study appears to be quite encouraging regarding the possibilities of using this method, which can be considered as an extension of the embedded cluster approach to covalent solids. Many applications to surface chemical reactivity studies can be imagined. © 1996 John Wiley & Sons, Inc.
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  • 227
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    International Journal of Quantum Chemistry 60 (1996), S. 1567-1576 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The contribution reports results of ongoing computations of various cage structures differing from the well-known buckminsterfullerene in the number of carbon atoms (C80) in their coordination or in the types of rings involved (C59). The computations have supplied a complete description of the seven isolated-pentagon-rule (IPR) isomers of C80 (i.e., a system not yet observed) at the semiempirical AM1 and SAM1 levels; their energetics was also evaluated at ab initio Hartree-Fock level in small basis sets. The ground-state structure of the system possesses a D5d symmetry, but at supposed synthetic conditions a structure of D2 symmetry is the most populated, i.e. temperature represents an important factor in the stability relationships. One of the IPR isomers exhibits an Ih topological symmetry, but it undergoes a Jahn-Teller distortion and its symmetry is actually reduced to D2. The C59 serves as an example of odd-numbered carbon clusters, and new rules are reported for the pentagon/hexagon pattern in the odd clusters, yielding a variable number of the pentagons. Moreover, other rings are considered and the computed ground state of the system in fact contains an eight-membered ring (while the next lowest species exhibits a nine-membered ring). Their relative stabilities are not very sensitive to temperature. Altogether 19 isomers of C59 are treated at the AM1 level. In contrast to even-numbered fullerenes, with odd fullerenes the cages cannot be built from three-coordinated carbon atoms only. Hence, we have to allow for two- or even four-coordinated atoms. For example, if we consider one two-coordinated carbon atom (and the rest three-coordinated) the number of pentagons drops to 10. If we allow for just one four-coordinated atom, the number of pentagons changes to 14. Let the number of two-coordinated carbon atoms be p, and the number of four-coordinated q. If we still allow only for pentagons and hexagons, it holds for the number of pentagons n5 = -2p + 2q + 12. © 1996 John Wiley & Sons, Inc.
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    International Journal of Quantum Chemistry 60 (1996), S. 1709-1718 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Various nitrogen clusters, Nx, are selected for the present theoretical study. The number of nitrogen atoms chosen in this work varies from x = 8 to x = 32. PM3, which is known as one of the best semiempirical methods, is selected for the self-consistent molecular orbital calculations. The geometrical optimization, vibrational frequencies, and thermochemical computations are all involved for various types of molecular nitrogen clusters. The results show that all Nx's belong to the category of stable high-energy compounds. Comparison of average bond energy and delocalization energy of all cases reveals that N20(Ih symmetry) is the most stable molecule among all the nitrogen clusters studied. In addition, our results show five-membered rings are the most favored in the structures of nitrogen clusters (Nx). © 1996 John Wiley & Sons, Inc.
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  • 229
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    International Journal of Quantum Chemistry 60 (1996), S. 1213-1213 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 230
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    International Journal of Quantum Chemistry 60 (1996), S. 1745-1764 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Interaction between the guanine-cytosine base pair and the episulfonium form of sulfur mustard (HD+) or the aziridinium form of nitrogen mustard (HN2+) was studied using the ab initio LCAO-MO method at the HF/6-31G level. The alkylation mechanism on the guanine N7 was analyzed by using a supermolecular modeling. Our stereostructural results associated with the molecular electrostatic potentials and highest occupied/lowest unoccupied molecular orbital (HOMO(SINGLEBOND)LUMO) properties show that in vacuum the alkylation of the N7 of guanine by HD+ in the agressive episulfonium form is a direct process without a transition state and of which the pathway is determined. Our study shows that interaction of guanine with the aziridinium form of HN2+ necessitates a transition state for the N7 alkylation route. When the N7 guanine alkylation by HD+ or HN2+ is achieved, about half of a positive charge moves from the alkylator toward the guanine in both cases. © 1996 John Wiley & Sons, Inc.
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  • 231
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    International Journal of Quantum Chemistry 60 (1996), S. 1797-1804 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A formalism is presented for quantifying the similarity between any two molecules. The chemical descriptor used for comparison is the molecular electrostatic potential at the van der Waals surface. Thus, both the spatial properties of a molecule and its chemical features are captured in this approach. For molecules that are geometrically alike, the most useful similarity measure stems from orienting the two species so that their physical surfaces are aligned as well as possible, without regard to chemical patterns. After this alignment is achieved, a single measure sensitive to the spatial distribution of the electrostatic potential is used to rank the electronic similarity. Molecular similarity measures are applied to the enzyme systems AMP deaminase and AMP nucleosidase in order to understand quantitatively why their respective transition-state inhibitors bind more tightly than do their substrates. © 1996 John Wiley & Sons, Inc.
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  • 232
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A procedure is described which leads to experimentally based models for the transition-state structures of enzyme-catalyzed reactions. Substrates for an enzymic reaction are synthesized with isotopically enriched atoms at every position in which bonding changes are anticipated at the enzyme-enforced transition state. Kinetic isotope effects are measured for each atomic substitution and corrected for diminution of the isotope effects from nonchemical steps of the enzymic mechanism. A truncated geometric model of the transition-state structure is fitted to the kinetic isotope effects using bond-energy bond-order vibrational analysis. Full molecularity is restored to the transition state while maintaining the geometry of the bonds which define the transition state. Electronic wave functions are calculated for the substrate and the transition-state molecules. The molecular electrostatic potential energies are defined for the van der Waal surfaces of substrate and transition state and displayed in numerical and color-coded constructs. The electronic differences between substrate and transition state reveal characteristics of the transition state which permits the extraordinary binding affinity of enzyme-transition state interactions. The information has been used to characterize several enzymatic transition states and to design powerfully inhibitory transition-state analogues. Enzymatic examples are provided for the reactions catalyzed by AMP deaminase, nucleoside hydrolase, purine nucleoside phosphorylase, and for several bacterial toxins. The results demonstrate that the combination of experimental, classical, and quantum chemistry approaches is capable of providing reliable transition-state structures and sufficient information to permit the design of transition-state inhibitors. © 1996 John Wiley & Sons, Inc.
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    International Journal of Quantum Chemistry 60 (1996), S. 1851-1863 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Using the information on the interatomic separations in a molecule, one can construct structural invariants that are the components of a molecular profile. The entries in the profile are derived by averaging different powers of the interatomic separations, suitably normalized so that the increasing powers do not dominate the sequence. Although only a few hundreds of structures have been so analyzed, no two different chemical structures were found to be characterized by the same sequences. A critical test for the conjecture that molecular profiles are unique is to consider structurally closely related systems that are very similar and have several similar properties. In this contribution we investigated the cuboctahedron and the accompanying polyhedron obtained by rotating half of the cuboctahedron against the other half, resulting in the so-called twist cutoctahedron. We show that even this pair of closely related structures has different profiles. We have also examined the generalized molecular profiles obtained by inserting n additional points along each edge of the polyhedra. The convergence of the profiles as n increases is discussed. It appears thus that these generalized molecular profiles, called line profiles or bond profiles, are likely to lead to a unique characterization of structures in which not only the geometry of atoms is recorded but also the geometry of the connectivity of the structure. © 1996 John Wiley & Sons, Inc.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1-32 
    ISSN: 0029-5981
    Keywords: finite volumes ; finite elements ; compressible flows ; unstructured grids ; hybrid grids ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A framework for the construction of node-centred schemes to solve the compressible Euler and Navier-Stokes equations is presented. The metric quantities are derived by exploiting some properties of C0 finite element shape functions. The resulting algorithm allows to implement both artificial diffusion and one-dimensional upwind-type discretizations. The proposed methodology adopts a uniform data structure for diverse grid topologies (structured, unstructured and hybrid) and different element shapes, thus easing code development and maintenance. The final schemes are well suited to run on vector/parallel computer architectures. In the case of linear elements, the equivalence of the proposed method with a particular finite volume formulation is demonstrated.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 81-97 
    ISSN: 0029-5981
    Keywords: porous media ; mixture theories ; fluid-saturated binary model ; incompressible constituents ; non-linear elasticity ; dynamic loading ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Based on the theory of porous media (mixture theories extended by the concept of volume fractions), a model describing the dynamical behaviour of a saturated binary porous medium is presented including both geometrical and material non-linearities. Transformed toward a weak formulation, the model equations are solved by use of the finite element method. Applications of the model range from one-dimensional linear problems to two-dimensional problems including the full dynamics and non-linearities.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 141-163 
    ISSN: 0029-5981
    Keywords: induction heating ; coupled problem ; three-dimensional analysis ; eddy current temperature analysis ; thin conducting sheet model ; eddy current boundary condition ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a special finite element formulation for the computer simulation of an inductive heating device for thin moving metal strips. The calculation includes both the electromagnetic field and the temperature distribution resulting from the losses of the induced currents. The electromagnetic field is described by an electric vector potential and a magnetic scalar potential, the induced eddy currents are represented by a special boundary condition for the magnetic scalar potential along the surface of the current-carrying strip. This avoids the necessity to discretize the thin secondary region. The thermal model includes the movement of the strip as well as convection and radiation as its surfaces. The field equations are discretized using the Galerkin variant of the Method of Weighted Residuals. The mutually coupled electromagnetic and temperature fields are then calculated using an iterative, staggered solution scheme. Comparisons between calculated and measured temperature profiles show the validity of the presented approach.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 33-50 
    ISSN: 0029-5981
    Keywords: finite element method ; shape optimization ; sensitivity analysis ; forming process ; optimal design ; forging ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We suggest a shape optimization method for a non-linear and non-steady-state metal forming problem. It consists in optimizing the initial shape of the part as well as the shape of the preform tool during a two-step forging operation, for which the shape of the second operation is known. Shapes are described using spline functions and optimal parameter values of the splines are searched in order to produce, at the end of the forging sequence, a part with a prescribed geometric accuracy, optimal metallurgical properties and for a minimal production cost. The finite element method, including numerous remeshing operations, is used for the simulation of the process. We suggest using a least-squares-type algorithm for the unconstrained optimization method (based on external penalty) for which we describe the calculation of the derivatives of the objective function. We show that it can reduce to calculations which are equivalent to the derivative calculations of steady-state processes and to evolution equations. Therefore, the computational cost of such an optimization is quite reasonable, even for complex forging processes. Lastly, in order to reduce the errors due to the numerous remeshings during the simulation, we introduce error estimation and adaptive remeshing methods with respect to the calculation of derivatives.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 165-184 
    ISSN: 0029-5981
    Keywords: curved unilateral contact ; augmented Lagrangian ; frictional contact element ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Based on a mixed formulation approach, a frictional contact element is proposed for the numerical solution of contact problems including strongly curved rigid obstacles. The implementation of the frictional contact element is analogous to that of a finite element. This feature facilitates its implementation in implicit finite element programmes, since the structure of the code need not be modified.For efficient modelling of the forming tool geometries by Computer Aided Geometric Design techniques and in order to achieve a high performance of the contact search, the numerical schemes of the frictional contact element operate directly on parametric polynomial surface patches. Thus, no discretization of curved contact surfaces is performed.Numerical simulations of deep drawing processes demonstrate the performance of the method in the case of large sliding increments upon curved tools and in the case of elasto-plasticity.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1097-1114 
    ISSN: 0029-5981
    Keywords: finite elements ; pneumatics ; air springs ; containers ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Many engineering structures completely surround and enclose gas filled volumes. The enclosed gas adds additional stiffness to the surrounding structure. This paper shows how to account for this effect by means of an augmented virtual work principle. The additional term augmenting the virtual work equilibrium statement for the structure is the virtual boundary work done by the pressure of the enclosed gas. The augmented equations are discretized using standard finite element methods, and the additional terms are discussed. The resulting ‘pneumatic’ finite element is shown to be analogous to regular structural finite elements. To assess the accuracy and efficiency and also to illustrate the applicability of the present formulation, a series of four examples was selected. In two of the examples, the behaviour of the end cap of a partially filled plastic food product container is studied. The numerical results using the pneumatic element compare well with an alternative Rayleigh-Ritz solution of the end cap behaviour. The other two examples represent the behaviour of a double bellows air spring shock absorber under static isothermal and dynamic adiabatic conditions. For the static isothermal case, an experimental study was performed with results in good agreement with the pneumatic element solutions. For the dynamic adiabatic loading case, the dynamic stiffness of the air spring was predicted using the pneumatic element. The numerical results agree with experimental data published in an air spring application guide. The examples illustrate that the pneumatic element formulation can be applied to the large deflection analysis of structures that enclose gas filled volumes.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1115-1136 
    ISSN: 0029-5981
    Keywords: particle tracking ; Lagrangian-Eulerian finite element methods ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a multi-dimensional particle tracking technique for applying the Lagrangian-Eulerian finite element method to solve transport equations in transient-state simulations. In the Lagrangian- Eulerian approach, the advection term is handled in the Lagrangian step so that the associated numerical errors can be considerably reduced. It is important to have an adequate particle tracking technique for computing advection accurately in the Lagrangian step. The particle tracking technique presented here is designed to trace fictitious particles in the real-world flow field where the flow velocity is either measured or computed at a limited number of locations. The technique, named ‘in-element’ particle tracking, traces fictitious particles on an element-by-element basis. Given a velocity field, a fictitious particle is traced one element by one element until either a boundary is encountered or the available time is completely consumed. For the tracking within an element, the element is divided into a desired number of subelements with the interpolated velocity computed at all nodes of the subelements. A fictitious particle, thus, is traced one subelement by one subelement within the element. The desired number of subelements can be determined based on the complexity of the flow field being considered. The more complicated the flow field is, the more subelements are needed to achieve accurate particle tracking results. A single-velocity approach can be used to efficiently perform particle tracking in a smooth flow field, while an average-velocity approach can be employed to increase the tracking accuracy for more complex flow fields.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1313-1340 
    ISSN: 0029-5981
    Keywords: iterative methods for linear systems ; preconditioning ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The preconditioned conjugate gradient algorithm is a well-known and powerful method used to solve large sparse symmetric positive definite linear systems. Such systems are generated by the finite element discretization in structural analysis but users of finite elements in this context generally still rely on direct methods. It is our purpose in the present work to highlight the improvement brought forward by some new preconditioning techniques and show that the preconditioned conjugate gradient method performs better than efficient direct methods.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1341-1356 
    ISSN: 0029-5981
    Keywords: constrained optimization ; feasible descent ; mathematical programming ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new Feasible Descent Cone (FDC) method for constrained optimization, previously restricted to linear objectives, is here generalized to include non-linear objective functions as well. In the basic and exact algorithm a sequence of descent steps is taken through the interior of the feasible region along the central lines of mathematically defined descent cones, constructed at successive boundary points. Here the basic algorithm is modified to allow for a minimum to occur within the interior, along a central descent ray in the case of non-linear objectives. A special interior procedure, with desirable mathematical properties, is adopted should the latter occur. To ensure economic implementation, the new generalized and exact algorithm, referred to as SSOPT2, is successively applied to a sequence of approximate quadratic subproblems. The overall generalized procedure that includes the successive application of SSOPT2 to the approximate subproblems, is referred to as the successive approximation version 2 algorithm (SAM2). The practical performance of SAM2 is assessed through its application to a number of small but otherwise representative test problems.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1357-1382 
    ISSN: 0029-5981
    Keywords: numerical reduced minimization ; non-uniform isoparametric mapping ; unmatched coefficient ; spurious constraint ; optimal minimization ; locking ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, the effects of various numerical integrations on the behaviour of C0-continuous beam elements under non-uniform isoparametric mapping are investigated by using numerical reduced minimization theory. The theory shows that stress recovery can be achieved by sampling stresses at the optimal integration points once a reduced integration is employed. It rationalizes the continued acceptance of the conventional reduced integration of constrained strain energy as one of remedies for locking due to spurious constraint.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1383-1403 
    ISSN: 0029-5981
    Keywords: crashworthiness ; homogenization ; topology design ; automotive structure optimization ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The topological optimization of components to maximize crash energy absorption for a given volume is considered. The crash analysis is performed using a DYNA3D finite element analysis. The original solid elements are replaced by ones with holes, the hole size being characterized by a so-called density (measure of the reduced volume). A homogenization method is used to find elastic moduli as a function of this density. Simpler approximations were developed to find plastic moduli and yield stress as functions of density.Optimality criteria were derived from an optimization statement using densities as the design variables. A resizing algorithm was constructed so that the optimality criteria are approximately satisfied. A novel feature is the introduction of an objective function based on strain energies weighted at specified times. Each different choice of weighting factors leads to a different structure, allowing a range of design possibilities to be explored.The method was applied to an automotive body rear rail. The original design and a new design of equal volume with holes were compared for energy absorption.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1419-1431 
    ISSN: 0029-5981
    Keywords: integral equations ; scattering ; boundary elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes a boundary integral equation (boundary element) method for the solution of a variety of transient acoustic problems. The spatial and temporal discretization employs quadratic isoparametric elements with high-order Gauss quadrature, and the ensuing equations are implicit. The implicit formulation both eliminates the instabilities reported in explicit treatments, and permits a freedom of choice of timestep which can reduce costs dramatically. The accuracy of the approach is demonstrated by comparison with the analytical solution for a sphere. Results for more demanding sphere-cone-sphere geometries extending to seven wavelengths long are presented, and compared to those obtained from a related frequency domain approach.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1405-1417 
    ISSN: 0029-5981
    Keywords: RTM ; control volume ; free surface ; porous medium ; sparse matrix ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An efficient numerical scheme is presented for simulating isothermal flow in resin transfer molding. The problem involves transient, free surface flow of an incompressible fluid into a non-deforming porous medium. A new variant of the Control Volume Finite Element (CVFE) algorithm is explained in detail. It is shown how the pressure solutions at each time step can be obtained by adding a single row and column to the Cholesky factorization of the stiffness matrix derived from a finite element formulation for the pressure field. This approach reduces the computation of a new pressure solution at each time step to essentially just two sparse matrix back-substitutions. The resulting performance improvement facilitates interactive simulation and the solution of inverse problems which require many simulations of the filling problem. The computational complexity of the calculation is bounded by O(n2⋅5), where n is the number of nodes in the finite element mesh. A 100-fold speedup over a conventional CVFE implementation was obtained for a 2213-node problem.
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    International Journal for Numerical Methods in Engineering 39 (1996) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1436-1436 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1433-1435 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1437-1454 
    ISSN: 0029-5981
    Keywords: large elastic deformations ; enhanced strain method ; finite elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The numerical simulation of processes undergoing finite deformations requires robust elements. For a broad range of applications these elements should have a good performance in bending dominated situations as well as in the case of incompressibility. The element should be insensitive against mesh distortions which frequently occurs during finite deformations. Furthermore, due to efficiency reasons a good coarse mesh accuracy in required in non-linear analysis. The QS6 element, developed in this paper, tries to fulfil the above-mentioned requirements. The performance is depicted by means of numerical examples.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1455-1473 
    ISSN: 0029-5981
    Keywords: transient loads ; advective-diffusive equations ; Petrov-Galerkin ; Galerkin Leask-Square ; boundary layers ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A Petrov-Galerkin formulation based on two different perturbations to the weighting functions is presented. These perturbations stabilize the oscillations that are normally exhibited by the numerical solution of the transient advective-diffusive equation in the vicinity of sharp gradients produced by transient loads and boundary layers. The formulation may be written as a generalization of the Galerkin Least-Square method.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1475-1489 
    ISSN: 0029-5981
    Keywords: meshing ; three-dimensional ; surfaces ; quadrilateral ; finite element ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper discusses the extension of the paving algorithm for all quadrilateral mesh generation to arbitrary three-dimensional trimmed surfaces. Methods of calculating angles, projecting elements, and detecting collisions between paving boundaries, for general surfaces are presented. Extensions of the smoothing algorithms for three dimensions are set forth. Advances in the use of scalar sizing functions are presented. These functions can be used to better approximate internal mesh density from boundary densities and surface characteristics.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 2155-2168 
    ISSN: 0029-5981
    Keywords: buckling ; composite laminated structures ; high-order element ; locking ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new high-order element for prebuckling and buckling of any laminated plane frame is developed. The kinematic approach involves a variety of high-order models with different powers of the thickness co-ordinate, and the derived stiffness matrix is based on a special power series, without a numerical process. It yields an exact formulation for high-order (first) models and improved formulations for higher-order (second and third) ones. A parametric study of the ‘locking’ phenomenon and the shear deformation effects was carried out for isotropic and laminated structures. It was found that the first-order model with an appropriate shear correction factor yielded results close to its higher-order counterparts.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 2265-2282 
    ISSN: 0029-5981
    Keywords: energy-conservation ; dynamics ; beams ; co-rotation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper describes an energy-conserving procedure for the implicit non-linear dynamic analysis of planar beam structures. The method is based on a form of co-rotational technique which is ‘external to the element’. A range of numerical results are presented which clearly demonstrate the improved numerical performance in comparison with more conventional techniques.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 2555-2573 
    ISSN: 0029-5981
    Keywords: 3-D boundary element method ; elastoplastic analysis ; hypersingular formulation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A 3-D hypersingular Boundary Integral Equation (BIE) of elastoplasticity is derived. Using this formulation the displacement rate gradients and the complete stress tensor on the boundary can be evaluated directly as opposed to the classical approach, where the shape functions derivatives are to be calculated. The regularization of strongly singular and hypersingular boundary integrals, as well as strongly singular domain integrals for a source point positioned on the boundary is carried out in a general manner. Arbitrary types of elements and arbitrary positions of the source point with respect to continuity requirements can be used. Numerical 3-D elastoplastic examples (notch and crack problems) illustrate the advantages of the proposed method.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 2337-2361 
    ISSN: 0029-5981
    Keywords: elastoplastic ; high-accuracy ; locking-free ; low-order ; nonlinear ; three-field functional ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a family of low-order high-accuracy three-dimensional brick elements. The elements are formulated via a three-field variational principle. The assumed (independent) strain field is constructed from two disjointed distributions. The first contains the lower-order distribution and its dimension is the minimum required to satisfy stability requirements. An energy constraint, which is enforced weakly at the element level, is used to relate the second distribution to the first. The stress field is chosen to a priori satisfy a similar energy constraint. As a result, internal constraints (e.g. incompressibility) are automatically satisfied by these fields, and locking behaviour is avoided. A J2-plasticity model illustrates the proposed elements' performance in nonlinear solids. The excellent performance of the proposed elements is demonstrated with numerous challenging examples, including many that are usually modelled by shell elements.
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    International Journal for Numerical Methods in Engineering 39 (1996) 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 2507-2508 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 2531-2554 
    ISSN: 0029-5981
    Keywords: boundary element method ; elastohydrodynamic lubrication ; layered contact ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a numerical routine to compute the contact characteristics of elastomer layered cylinders lubricated by isoviscous liquids. The indentation of the elastic layer is calculated from boundary integral equations which are solved by linear and quadratic boundary element methods for a finite plane model and a circular representation of the junction. The hydrodynamic equation is also transformed into a boundary integral equation and solved by Simpson's rule. Some factors which possibly affect numerical accuracy are examined. Examples for finite plane and circular layer are analysed with reference to parameters for printing press roller contact, in which results are obtained for the indentation, film thickness and liquid pressure, as well as internal stresses through the simultaneous solution of the elasticity and hydrodynamic equations. The results show that high precision is easily achieved and the method is efficient for such layered problems.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 2789-2802 
    ISSN: 0029-5981
    Keywords: finite elements ; three-dimensional elasticity ; equilibrium formulations ; hybrid finite elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper an approach to the formulation of equilibrium elements for the analysis of three-dimensional elasticity problems is presented.This formulation is an extension of the approach previously proposed for the analysis of two-dimensional elasticity problems. The general aspects of the formulation remain unchanged when applied to the new problem, but new points are considered, namely the way to perform volume integrations for general elements and the techniques used to obtain the self-equilibrated three-dimensional stress approximation functions.The numerical behaviour of such elements is presented and discussed.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 2837-2862 
    ISSN: 0029-5981
    Keywords: special boundary integral formulation ; design sensitivity analysis (DSA) ; direct differentiation approach (DDA) ; three-dimensional conduction heat transfer ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A special boundary integral formulation had been proposed to analyse many engineering problems of conduction heat transfer in complex three-dimensional geometries (closely spaced surface and circular hole in infinite domain or simple modification of it) by Rezayat and Burton. One example of such geometries is the mold sets in the injection molding process. In this paper, an efficient and accurate approach for the design sensitivity analysis (DSA) is presented for these kinds of problems in the similar complex geometries using the direct differentiation approach (DDA) based on the above special boundary integral formulation. The present approach utilizes the implicit differentiation of the boundary integral equations with respect to the design variables (radii and locations of circular holes) to yield the sensitivity equations. A sample problem (heat transfer of injection molding cooling system) is solved to demonstrate the accuracy of the present sensitivity analysis formulation. Although the techniques introduced here are applied to a particular problem in heat transfer of injection molding cooling system, their potential application is quite broad.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 2921-2944 
    ISSN: 0029-5981
    Keywords: wavelet orthogonal bases ; wavelet-Galerkin method ; Burgers' equation ; numerical method ; approximation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes exact evaluations of various finite integrals whose integrands involve products of Daubechies' compactly supported wavelets and their derivatives and/or integrals. These finite integrals play an essential role in the wavelet-Galerkin approximation of differential or integral equations on a bounded interval.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 2973-2985 
    ISSN: 0029-5981
    Keywords: co-rotational frame ; convected bases ; integration of the spin ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new algorithm is proposed for integrating the spin in the frame of large deformation analysis. The method is based on the integration of a matrix relation, obtained from an adapted decomposition of the deformation gradient, and directly written in convected co-ordinates. The input of this algorithm is either the Gram matrix at any time (if a kinematical method is used, for instance) or more generally, the incremental deformation gradient, and the output is the required rotation matrix on convected bases. The result takes a very simple form in the important case of classical shells.
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 3195-3215 
    ISSN: 0029-5981
    Keywords: modified effective capacitance ; solidification ; tetrahedral elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper a new formulation for modelling solidification is discussed. The formulation has similar features to both the apparent and effective heat capacitance methods used for solidification problems where conduction predominates over other heat transfer mechanisms. The main feature of the new method is that a modified form of effective heat capacitance is calculated from the solution of non-linear equations that describe the energy loss for linear tetrahedral finite elements. This approach ensures that the predicted temperature field corresponds exactly with the energy loss and so providing an extremely stable formulation. The method is tested against a range of problems including some with non-linear liquid fractions. The predictions are compared against known analytical solutions and the method is shown to provide reasonable accuracy even for relatively large time-steps. A comparison is made between the method and the well-known temporal and spatial approximations of apparent heat capacitance, and effective capacitance. Accuracy is maintained over a greater variation in time-step and mesh density with comparable computational requirements. In addition, the method lends itself to the use of relatively simple bisection techniques for the solution of the non-linear finite element equations. Also demonstrated is the method's innate ability to predict energy loss to a high degree of accuracy for large time steps.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 3049-3064 
    ISSN: 0029-5981
    Keywords: mold cooling ; injection molding ; finite element method ; three-dimensional ; Jacobi conjugate gradient ; matrix-free algorithm ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A methodology is presented to simulate the three-dimensional heat transfer within a mold during the injection molding process. The mold cooling analysis assists cooling channel design and paves the way for part shrinkage and warpage analysis. The transient temperature distributions in the mold and the polymer part are simultaneously computed by Galerkin Finite Element Method (GFEM) using a matrix-free Jacobi Conjugate Gradient (JCG) scheme. The numerical method presented here is efficient and has shown to require a fraction of the memory and computing time required by conventional methods. The matrix-free algorithm is initially validated using an injection mold designed to produce a plaque with a molded-in hole. Subsequently, the method is further applied to a representative automotive plastic component.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 2907-2920 
    ISSN: 0029-5981
    Keywords: sensitivity analysis ; error estimates ; mesh refinement ; hypersingular integrals ; boundary element method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The subject of this paper is the sensitivity analysis of approximate boundary element solutions with respect to the positions of the collocation points. The direct differentiation approach is considered here and the analysis is performed analytically. Since only the collocation points are perturbed, the shape of the body and the corresponding discretization remain unaltered. This aspect makes the present work quite different in spirit with respect to earlier analyses on shape sensitivities. Sensitivities of approximate BEM solutions with respect to the positions of collocation points are shown to be related to the residual of hypersingular integral equations. Numerical results confirm that the present approach can be seen as the analytical counterpart of an adaptive scheme for mesh refinement presented by the same author in some recent papers. Some other advantages of the present approach over the former one are also outlined.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 3217-3217 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 3327-3349 
    ISSN: 0029-5981
    Keywords: mesh generation ; hexahedral ; whisker weaving ; duality ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper introduces a new algorithm called whisker weaving for constructing unstructured, all-hexahedral finite element meshes. Whisker weaving is based on the Spatial Twist Continuum (STC), a global interpretation of the geometric dual of an all-hexahedral mesh. Whisker weaving begins with a closed, all-quadrilateral surface mesh bounding a solid geometry, then constructs hexahedral element connectivity advancing into the solid. The result of the whisker weaving algorithm is a complete representation of hex mesh connectivity only: Actual mesh node locations are determined afterwards.The basic step of whisker weaving is to form a hexahedral element by crossing or intersecting dual entities. This operation, combined with seaming or joining operations in dual space, is sufficient to mesh simple block problems. When meshing more complex geometries, certain other dual entities appear such as blind chords, merged sheets, and self-intersecting chords. Occasionally specific types of invalid connectivity arise. These are detected by a general method based on repeated STC edges. This leads into a strategy for resolving some cases of invalidities immediately.The whisker weaving implementation has so far been successful at generating meshes for simple block-type geometries and for some non-block geometries. Mesh sizes are currently limited to a few hundred elements. While the size and complexity of meshes generated by whisker weaving are currently limited, the algorithm shows promise for extension to much more general problems.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 3367-3390 
    ISSN: 0029-5981
    Keywords: finite plasticity ; single crystals ; multisurface plasticity ; active set search ; exponential map ; stress update algorithm ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a new stress update algorithm for large-strain rate-independent single-crystal plasticity. The theoretical frame is the well-established continuum slip theory based on the multiplicative decomposition of the deformation gradient into elastic and plastic parts. A distinct feature of the present formulation is the introduction and computational exploitation of a particularly simple hyperelastic stress response function based on a further multiplicative decomposition of the elastic deformation gradient into spherical and unimodular parts, resulting in a very convenient representation of the Schmid resolved shear stresses on the crystallographic slip systems in terms of a simple inner product of Eulerian vectors. The key contribution of this paper is an algorithmic formulation of the exponential map exp: sl(3) → SL(3) for updating the special linear group SL(3) of unimodular plastic deformation maps. This update preserves exactly the plastic incompressibility condition of the anisotropic plasticity model under consideration. The resulting fully implicit stress update algorithm treats the possibly redundant constraints of single-crystal plasticity by means of an active set search. It exploits intrinsically the simple representation of the Schmid stresses by formulating the return algorithm and the associated consistent elastoplastic moduli in terms of Eulerian vectors updates. The performance of the proposed algorithm is demonstrated by means of a representative numerical example.
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 3663-3677 
    ISSN: 0029-5981
    Keywords: matrix condition ; heat equation ; discontinuous coefficients ; error stability ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The traditional tridiagonal matrix approximating the one-dimensional heat equation is ill-conditioned when heat conductivity changes radically. An algebraic reformulation of the tridiagonal produces a well-conditioned matrix. Additional variables are rates q=-kux at interfaces between radical changes in k. A reduced matrix amounts to a coarse approximation.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 3679-3703 
    ISSN: 0029-5981
    Keywords: 3-D fracture ; interface ; boundary element ; singular integration ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Mixed-mode fractures of arbitrary orientation with respect to a planar bimaterial interface have been effectively modelled using a surface integral approach. By requiring only that the surface of the fracture be discretized, the surface integral method circumvents the practical difficulties associated with having to mesh the interacting dual singularities in stress along the three-dimensional (3-D) crack front and at the interface. The key elements of this numerical capability are discussed in detail. These include: the derivation of the fundamental solutions for a generalized fracture event near a planar bimaterial interface, formulation of the governing integral equation including its decomposition into singular and non-singular terms, development of analytical and numerical techniques for performing the singular integrations, and efficient numerical integration of the non-singular terms using non-dimensionalized surface approximations of the dipole solutions. The problem of a pressurized planar crack near a bimaterial interface was used to assess convergence. The effect of material contrast and crack shape on tendencies for crack growth were also examined.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 3453-3474 
    ISSN: 0029-5981
    Keywords: plate ; finite element ; locking ; non-linear ; buckling ; vibrations ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new eight-node C0 membrane-plate quadrilateral finite element is presented to analyse static and dynamic moderately large deflections of moderately thick laminates. The finite element is based on the Reissner- Mindlin plate theory and on previous works for the shear-bending (plate) part, which has been described in a previous paper, Reference 10. In the paper, the novelty is in the way of improving isoparametric membrane response without adding zero-energy modes, and the moderately large deflection static and dynamic analysis of laminates based on von Karman's assumptions. Finally, some numerical simulations are presented in statics and in dynamics for laminates, including buckling analysis and membrane-plate coupling effects. Among a large variety of finite elements which have been proposed during the two last decades, interest in the present element lies in its simplicity implementation, its efficiency without any correction factors and spurious energy modes, and (also) the fact it is fully standard from an engineering view point.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 3475-3495 
    ISSN: 0029-5981
    Keywords: structural dynamics ; time finite elements ; Hermitian shape functions ; unconditionally stable algorithms ; higher-order accurate algorithms ; time-step integration ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, single step time finite elements using the cubic Hermitian shape functions to interpolate the solution over a time interval are considered. The second-order differential equations are manipulated directly. Both the effects of modal damping and external excitation are considered. The accuracy of the solutions at the end of the time interval and the interpolated solutions within the time interval is investigated. The weighted residual approach is adopted to derive the time-integration algorithms. Instead of specifying the weighting functions, the weighting parameters are used to control the characteristics of the time finite elements. The weighting parameters are chosen to eliminate the higher-order truncation error terms or to enforce the asymptotic annihilation condition. A one-parameter family of third-order accurate asymptotically annihilating algorithms and another one-parameter family of fourth-order accurate non-dissipative algorithms are presented. The ranges of the weighting parameters for unconditionally stable algorithms are given. It is found that one of the members in each family corresponds to the Padé approximants of the exponential function in solving the first-order differential equations. Some of the existing unconditionally stable higher-order accurate algorithms are re-derived by the present unified approach.
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 3553-3569 
    ISSN: 0029-5981
    Keywords: finite/infinite element method ; infinite element ; semi-infinite problem ; soil-structure interaction ; wave propagation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Two drawbacks exist with the infinite elements used for simulating the unbounded domains of semi-infinite problems. The first is the lack of an adequate measure for calculating the decay parameter. The second is the frequency-dependent characteristic of the finite/infinite element mesh used for deriving the impedance matrices. Based on the properties of wave propagation, a scheme is proposed in this paper for evaluating the decay parameter. In addition, it is shown that by the method of dynamic condensation, the far-field impedance matrices for waves of lower frequencies can be obtained repetitively from the one for waves of the highest frequency, using exactly the same finite/infinite element mesh. Such an approach ensures that accuracy of the same degree can be maintained for waves of all frequencies within the range of consideration. Effectiveness of the proposed method is demonstrated in the numerical examples through comparison with previous results.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 3867-3887 
    ISSN: 0029-5981
    Keywords: discrete Kirchhoff theory ; shell element ; semiloof element ; non-linear shell analysis ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the formulation of flat shell elements it is difficult to achieve inter-element compatibility between membrane and transverse displacements for non-coplanar elements. Many elements lack proper nodal degrees of freedom to model intersections making the assembly of elements troublesome. A flat triangular shell element is established by a combination of a new plate bending element DKTL and the well-known linear membrane strain element LST, and for this element the above-mentioned deficiencies are avoided. The plate bending element DKTL is based on Discrete Kirchhoff Theory and Loof nodes. The nodal configuration of the element is similar to the SemiLoof element, and the formulation is an improvement of a previous formulation. The element is used for both linear statics, linear buckling and geometrical non-linear analysis, and numerical examples are presented to show the robustness, accuracy and quick convergence of the element.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 3931-3931 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 3985-3998 
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    Keywords: structural dynamics ; time stepping ; collocation ; Gauss points ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: When a cubic function is interpolated between the prescribed initial displacement and velocity and the exact displacement and velocity at the end of a time step for a single degree of freedom system, the error, or residual, in the governing equation is zero at a number of times. It is shown that for a general undamped system, in the limit as the time step approaches zero these times correspond to Gauss points. This observation is verified by considering a general collocation procedure in which the displacement in any time step is approximated as a cubic function of time, with two coefficients chosen to satisfy the displacement and velocity at the beginning of the time step with the other two coefficients being chosen to satisfy the governing differential equation at any two times. It is shown that optimum accuracy is obtained if these points are the Gauss points. Detailed expressions are then presented for this particular case, and stability of the algorithm is investigated showing that the procedure is conditionally stable. For time steps which are a small proportion of the least period of vibration of the structure, the algorithm is considered to be the most accurate possible procedure based on cubic approximation of the displacement.
    Additional Material: 3 Ill.
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  • 281
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 3999-4020 
    ISSN: 0029-5981
    Keywords: sparse matrices ; frontal methods ; Gaussian elimination ; finite-element equations ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The multiple front algorithm is an extension of the frontal method to allow parallelism to be exploited in the solution process. The finite-element domain is partitioned into a number of subdomains and a frontal decomposition is performed on each subdomain separately. For a given partitioning of the domain, the efficiency of the multiple front algorithm depends on the ordering of the elements within each subdomain. We look at the limitations of existing element reordering algorithms when applied to a subdomain and consider how these limitations may be overcome. Extensive numerical experiments are performed on a range of practical problems and, on the basis of the results, we propose a new element resequencing algorithm for use with a multiple front algorithm.
    Additional Material: 6 Tab.
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  • 282
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 4039-4061 
    ISSN: 0029-5981
    Keywords: finite element method ; optimal mesh ; strategy ; refinement ; error estimation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Five Adaptive Modification Strategies (AMSs) are studied as means to obtain nearly optimal meshes using an adaptive finite element modelling system based on the h-version of the FEM. These strategies include the method traditionally seem in the literature as well as four additional methods. The five strategies are tested over five numerical examples, one of them producing convergence oscillations in one example. The principal characteristic of our system is that it permits the user to control certain parameters of the adaptive process, which contributes to an improvement in the results.
    Additional Material: 11 Ill.
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  • 283
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    Numerical Linear Algebra with Applications 3 (1996), S. 1-20 
    ISSN: 1070-5325
    Keywords: preconditioning saddle-point problems ; eigenvalue estimation ; mixed finite element method ; minimum residual method ; second-order elliptic problems ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider saddle-point problems that typically arise from the mixed finite element discretization of second-order elliptic problems. By proper equivalent algebraic operations the considered saddle-point problem is transformed to another saddle-point problem. The resulting problem can then be efficiently preconditioned by a block-diagonal matrix or by a factored block-matrix (the blocks correspond to the velocity and pressure, respectively). Both preconditioners have a block on the main diagonal that corresponds to the bilinear form(δ is a positive parameter) and a second block that is equal to a constant times the identity operator. We derive uniform bounds for the negative and positive eigenvalues of the preconditioned operator. Then any known preconditioner for the above bilinear form can be applied. We also show some numerical experiments that illustrate the convergence properties of the proposed technique.
    Additional Material: 2 Tab.
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  • 284
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    Numerical Linear Algebra with Applications 3 (1996) 
    ISSN: 1070-5325
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 285
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    Numerical Linear Algebra with Applications 3 (1996), S. 65-80 
    ISSN: 1070-5325
    Keywords: boundary value problem ; boundary element method ; preconditioning ; iterative method ; fast Fourier transform ; parallel algorithm ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The parallel version of precondition iterative techniques is developed for matrices arising from the panel boundary element method for three-dimensional simple connected domains with Dirichlet boundary conditions. Results were obtained on an nCube-2 parallel computer showing that preconditioned iterative methods are very well suited also in three-dimensional cases for implementation on an MIMD computer and that they are much more efficient than usual direct solution techniques.
    Additional Material: 6 Ill.
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  • 286
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    Numerical Linear Algebra with Applications 3 (1996), S. 91-93 
    ISSN: 1070-5325
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 287
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    Numerical Linear Algebra with Applications 3 (1996), S. 113-124 
    ISSN: 1070-5325
    Keywords: iterative methods ; linear systems ; multisplittings ; overlap ; parallel algorithms ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Parallel two-stage multisplitting methods with overlap for the solution of linear systems of algebraic equations are studied. It is shown that, under certain hypotheses, the method with overlap is asymptotically faster than that without overlap. Experiments illustrating this phenomenon are presented.
    Additional Material: 2 Ill.
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  • 288
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    Numerical Linear Algebra with Applications 3 (1996), S. 91-111 
    ISSN: 1070-5325
    Keywords: boundary integral operators ; domain decomposition ; interface operators ; fast elliptic problem solvers ; parallel algorithms ; preconditioning ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper a method for fast computations with the inverse to weakly singular, hypersingular and double layer potential boundary integral operators associated with the Laplacian on Lipschitz domains is proposed and analyzed. It is based on the representation formulae suggested for above-mentioned boundary operations in terms of the Poincare-Steklov interface mappings generated by the special decompositions of the interior and exterior domains. Computations with the discrete counterparts of these formulae can be efficiently performed by iterative substructuring algorithms provided some asymptotically optimal techniques for treatment of interface operators on subdomain boundaries. For both two- and three-dimensional cases the computation cost and memory needs are of the order O(N logp N) and O(N log2 N), respectively, with 1 ≤ p ≤ 3, where N is the number of degrees of freedom on the boundary under consideration (some kinds of polygons and polyhedra). The proposed algorithms are well suited for serial and parallel computations.
    Additional Material: 2 Ill.
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  • 289
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    Numerical Linear Algebra with Applications 3 (1996), S. 173-177 
    ISSN: 1070-5325
    Keywords: diagonally dominant matrix ; determinant ; norm ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A property of strictly diagonally dominant matrices and a generalization of a Varga's bound for ∥ A-1∥∞ to the case ∥ A-1B∥∞ are given and the two-sided bounds for the determinants of strictly diagonally dominant matrices are derived
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  • 290
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    Numerical Linear Algebra with Applications 3 (1996), S. 125-145 
    ISSN: 1070-5325
    Keywords: orthogonalization ; QR factorization ; polar decomposition ; subspace tracking ; error analysis ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the problem of computing Uk = QkUk-1(where U0 is given) in finite precision (εM = machine precision) where U0 and theQi are known to be unitary. The problem is that Ûk, the computed product may not be unitary, so one applies an O(n2) orthogonalizing step after each multiplication to(a) prevent Ûk from drifing too far from the set of untary matrices(b) prevent Ûk from drifting too far from Uk the true product.Our main results are1. Scaling the rows to have unit length after each multiplication (the cheaptest of the algorithms considered) is usually as good as any other method with respect to either of the criteria (a) or (b).2. A new orthogonalization algorithm that guarantees the distance of Ûk (k = 1, 2, …) to the set of unitary matrices is bounded by n3.5εM for any choice of Qi.
    Additional Material: 4 Ill.
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  • 291
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    Numerical Linear Algebra with Applications 3 (1996) 
    ISSN: 1070-5325
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 292
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    Numerical Linear Algebra with Applications 3 (1996), S. 525-542 
    ISSN: 1070-5325
    Keywords: potential flow problem in porous media ; mixed-hybrid formulation trilateral prismatic elements ; symmetric indefinite linear systems ; minimal residual method ; rate of convergence ; asymptotic convergence factor ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In the paper the potential fluic flow problem in porous media using Darcy's law and the continuity equation is solved. Mixed-hybrid finite element formulation based on general trilateral prismatic elements is considered. Spectral properties of resulting symmetric indefinite system of linear equations are examined. Minimal residual method for the solution of systems with a symmetric indefinite matrix is applied. The rate of convergence and the asymptotic convergence factor which depend on the eigenvalue distribution of the system matrix are estimated.
    Additional Material: 2 Ill.
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  • 293
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    Numerical Linear Algebra with Applications 3 (1996) 
    ISSN: 1070-5325
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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  • 294
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    Numerical Linear Algebra with Applications 3 (1996), S. 239-249 
    ISSN: 1070-5325
    Keywords: non-linear equations ; global convergence ; Lagrangians ; non-linear programming ; Lagrangian globalization ; detour potentials ; homotopy methods ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The Lagrangian globalization (LG) method for non-linear equation-solving proposed in [10] is developed through theoretical analysis, the formulation of a particular LG algorithm, and a numerical illustration. New merit functions (termed detour potentials) for non-linear equation-solving, which broaden the LG concept, are also defined.
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  • 295
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    Numerical Linear Algebra with Applications 3 (1996), S. 251-254 
    ISSN: 1070-5325
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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  • 296
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    Numerical Linear Algebra with Applications 3 (1996), S. 21-44 
    ISSN: 1070-5325
    Keywords: first-order PDEs ; iterative methods ; preconditioners ; Toeplitz ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Preconditioners to nonsymmetric, nondiagonally dominant systems of equations are constructed and examined numerically. The preconditioners are based on a Toeplitz approach with a certain symmetry that we define. The inversion of the preconditioners is defined through a Fast Modified Sine Transform. As a model problem we study the systems of equations arising from a implicit time-discretization with a large time-step of a scalar hyperbolic PDE.
    Additional Material: 17 Ill.
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    Numerical Linear Algebra with Applications 3 (1996), S. 45-64 
    ISSN: 1070-5325
    Keywords: Toeplitz least squares problems ; circulant preconditioned conjugate gradient method ; deconvolution ; image restoration ; atmospheric imaging ; medical imaging ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper, we propose a method to generalize Strang's circulant preconditioner for arbitrary n-by-n matrices An. The th column of our circulant preconditioner Sn is equal to the th column of the given matrix An. Thus if An is a square Toeplitz matrix, then Sn is just the Strang circulant preconditioner. When Sn is not Hermitian, our circulant preconditioner can be defined as . This construction is similar to the forward-backward projection method used in constructing preconditioners for tomographic inversion problems in medical imaging. We show that if the matrix An has decaying coefficients away from the main diagonal, then is a good preconditioner for An. Comparisons of our preconditioner with other circulant-based preconditioners are carried out for some 1-D Toeplitz least squares problems: min ∥ b - Ax∥2. Preliminary numerical results show that our preconditioner performs quite well, in comparison to other circulant preconditioners. Promising test results are also reported for a 2-D deconvolution problem arising in ground-based atmospheric imaging.
    Additional Material: 5 Ill.
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  • 298
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    Communications in Numerical Methods in Engineering 12 (1996) 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 299
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    Communications in Numerical Methods in Engineering 12 (1996), S. 75-76 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 300
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    Communications in Numerical Methods in Engineering 12 (1996), S. 1-11 
    ISSN: 1069-8299
    Keywords: interval parameters ; interval static responses ; interval linear equations ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A structure subjected to interval parameters and interval loads which are unknown, except for the fact that they belong to given intervals, is studied and the displacement bound estimation is given. These parameters are uncertain, and yet they are not treated as being random since no information is available on their probabilistic characteristics. A set of possible states of the system is described by interval matrices. The perturbation method is employed as a simple analytical tool for determining static responses - interval displacements of finite element equilibrium equations with interval parameters. The numerical results show that the proposed method is extremely effective.
    Additional Material: 1 Ill.
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