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  • 1
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1511-1536 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Iterative techniques for the solution of the algebraic equations associated with the direct boundary element analysis (BEA) method are discussed. Continuum structural response analysis problems are considered, employing single- and multi-zone boundary element models with and without zone condensation. The impact on convergence rate and computer resource requirements associated with the sparse and blocked matrices, resulting in multi-zone BEA, is studied. Both conjugate gradient and generalized minimum residual preconditioned iterative solvers are applied for these problems and the performance of these algorithms is reported. Included is a quantification of the impact of the preconditioning utilized to render the boundary element matrices solvable by the respective iterative methods in a time competitive with direct methods. To characterize the potential of these iterative techniques, we discuss accuracy, storage and timing statistics in comparison with analogous information from direct, sparse blocked matrix factorization procedures. Matrix populations that experience block fill-in during the direct decomposition process are included. With different degrees of preconditioning, iterative equation solving is shown to be competitive with direct methods for the problems considered.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 2157-2187 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Accounts of the symmetric Galerkin approach to boundary element analysis (BEA) have recently been published. This paper attempts to add to the understanding of this method by addressing a series of fundamental issues associated with its potential computational efficiency. A new symmetric Galerkin theoretical formulation for both the (harmonic) heat conduction and the (biharmonic) elasticity problem that employs regularized singular and hypersingular boundary integral equations (BIEs) is presented. The novel use of regularized BIEs in the Galerkin context is shown to allow straightforward incorporation of curved, isoparametric elements. A symmetric reusable intrinsic sample point (RISP) numerical integration algorithm is shown to produce a Galerkin (i.e. double) integration strategy that is competitive with its counterpart (i.e. singular) integration procedure in the collocation BEA approach when the time saved in the symmetric equation solution phase is also taken into account. This new formulation is shown to be capable of employing hypersingular BIEs while obviating the requirement of C1 continuity, a fact that allows the employment of the popular continuous element technology. The behaviour of the symmetric Galerkin BEA method with regard to both direct and iterative equation solution operations is also addressed. A series of example problems are presented to quantify the performance of this symmetric approach, relative to the more conventional unsymmetric BEA, in terms of both accuracy and efficiency. It is concluded that appropriate implementations of the symmetric Galerkin approach to BEA indeed have the potential to be competitive with, if not superior to, collocation-based BEA, for large-scale problems.
    Additional Material: 16 Ill.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 1651-1672 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The performance of a number of preconditioned Krylov methods is analysed for a large variety of boundary element formulations. Low- and high-order element, two-dimensional (2-D) and three-dimensional 3-D, regular, singular and hypersingular, collocation and symmetric Galerkin, single- and multi-zone, thermal and elastic, continuous and discontinuous boundary formulations with and without condensation are considered. Preconditioned Conjugate Gradient (CG) solvers in standard form and a form effectively operating on the normal equations (CGN), Generalized Minimal Residual (GMRES), Conjugate Gradient Squared (CGS) and Stabilized Bi-conjugate Gradient (Bi-CGSTAB) Krylov solvers are employed in this study. Both the primitive and preconditioned matrix operators are depicted graphically to illustrate the relative amenability of the alternative formulations to solution via Kryiov methods, and to contrast and explain their computational performances. A notable difference between 2-D and 3-D BEA operators is readily visualized in this manner. Numerical examples are presented and the relative conditioning of the various discrete BEA operators is reflected in the performance of the Krylov equation solvers. A preconditioning scheme which was found to be uncompetitive in the collocation BEA context is shown to make iterative solution of symmetric Galerkin BEA problems more economical than employing direct solution techniques. We conclude that the preconditioned Krylov techniques are competitive with or superior to direct methods in a wide range of boundary formulated problems, and that their performance can be partially correlated with certain problem characteristics.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2795-2811 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The structural design sensitivity analysis of a two-dimensional continuum using conforming (continuous) boundary elements is investigated. Implicit differentiation of the discretized boundary integral equations is performed to obtain design sensitivities in an efficient manner by avoiding the factorization of the perturbed matrices. A singular formulation of the boundary element method is used. Implicit differentiation of the boundary integral equations produces terms that contain derivatives of the fundamental solutions employed in the analysis. The behaviour of the singularity of these derivatives of the boundary element kernel functions with respect to the design variables is investigated. A rigid body motion technique is presented to obtain the singular terms in the resulting sensitivity matrices, thus avoiding the problems associated with their numerical integration. A formulation for obtaining the design sensitivities of the continua under body forces of the gravitational and centrifugal types is also presented. The design sensitivity results are seen to be of the same order of accuracy as the boundary element analysis results. Numerical data comparing the performance of conforming and non-conforming formulations in the calculation of design sensitivities are also presented. The accuracy of the present results is demonstrated through comparisons with existing analytical results.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1661-1676 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents an algorithm that provides an order of magnitude gain in the computational performance of the numerical integration of the boundary integral equations for three dimensional analysis. Existing algorithms for numerical integration have strategically clustered integration sample points based on the relative proximity of the load points to the boundary element being integrated using element subdivision or element co-ordinate transformation. The emphasis in these techniques has been on minimizing the number of sample points required to obtain a given level of accuracy. The present algorithm, while closely following the spirit of these earlier approaches, employs a discrete number of sets of predetermined, customized, near-optimum, sample point quantities associated with the intrinsic boundary element. The ability created by this approach to reuse sample point geometric information of the actual element allows for the realization of substantive computational economy. This algorithm provides accurate and efficient numerical results both when load points are far from, and when they are on the boundary element being integrated. Numerical results are provided to demonstrate the substantial economy achieved through the use of the present algorithm.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 38 (1995), S. 2839-2866 
    ISSN: 0029-5981
    Keywords: shape design sensitivity ; material derivative-adjoint variable technique ; boundary elements ; performance functional ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A general approach to shape design sensitivity analysis of three- and two-dimensional elastic solid objects is developed using the material derivative-adjoint variable technique and boundary element method. The formulation of the problem is general and first-order sensitivities in the form of boundary integrals for the effect of boundary shape variations are derived for an arbitrary performance functional. Second-order quadrilateral surface elements (for 3-D problems) and quadratic boundary elements (for 2-D problems) are employed in the solution of primary and adjoint systems and discretization of the boundary integral expressions for sensitivities. The accuracy of sensitivity information is studied for selected global performance functionals and also for boundary state fields at discrete points. Numerical results are presented to demonstrate the accuracy and efficiency of this approach.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
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