International Journal for Numerical Methods in Engineering, Vol. 50, No. 9, pp. 2233-2269, 2001
M.K. Chati
Department of Theoretical and Applied Mechanics, Cornell University, Ithaca, NY 14853,
U.S.A.
G.H. Paulino,
Department of Civil and Environmental Engineering, University of Illinois
at Urbana-Champaign, 2209 Newmark Laboratory, 205 N. Mathews Avenue, Urbana,
IL 61801, U.S.A.
S. Mukherjee
Department of Theoretical and Applied Mechanics, Cornell University, Ithaca, NY 14853,
U.S.A.
Abstract
The standard (singular) boundary node method (BNM) and the novel hypersingular
boundary node method (HBNM) are employed for the usual and adaptive solutions of
three-dimensional potential and elasticity problems. These methods couple boundary
integral equations with moving least squares interpolants while retaining the
dimensionality advantage of the former and the meshless attribute of the latter. The
"hypersingular residuals", developed for error estimation in the mesh-based
collocation boundary element method (BEM) and symmetric Galerkin BEM are extended to the
meshless BNM setting. A simple "a posteriori" error estimation and an
effective adaptive refinement procedure are presented. The implementation of all the
techniques involved in this work are discussed, which include aspects regarding parallel
implementation of the BNM and HBNM codes. Several numerical examples are given and
discussed in detail. Conclusions are inferred and relevant extensions of the
methodology introduced in this work are provided. Two appendices, dealing with the
evaluation of nearly singular integrals and implementation of a scheme for obtaining
displacement gradients on the surface of a body, supplement the paper.
Key words: meshless methods, boundary node method (BNM), hypersingular boundary node method (HBNM), singular residuals, hypersingular residuals, error estimates, adaptivity, parallel computing
Representative Results
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Framework | |
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Progressive Adaptation: Potential Example | |
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Multilevel Refinement: Potential Example | |
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Propressive Adaptation: Elasticity Example | |
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Multilevel Refinement: Elasticity Example |