Reproducing polynomial particle methods for boundary integral equations

Authors:
Hae-Soo Oh;Christopher Davis;June G. Kim;Yonghoon Kwon
Affiliations:
Department of Mathematics & Statistics, University of North Carolina at Charlotte, Charlotte, USA 28223;Department of Mathematics & Statistics, University of North Carolina at Charlotte, Charlotte, USA 28223;Department of Mathematics, Kangwon National University, Chunchon, Korea 200-701;Department of Mathematics, Pohang University of Science and Technology, Pohang, Korea 790-784
Venue:
Computational Mechanics
Year:
2011

Citing 6
Cited 1

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Meshfree Particle Methods in the Framework of Boundary Element Methods for the Helmholtz Equation

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Abstract

Since meshless methods have been introduced to alleviate the difficulties arising in conventional finite element method, many papers on applications of meshless methods to boundary element method have been published. However, most of these papers use moving least squares approximation functions that have difficulties in prescribing essential boundary conditions. Recently, in order to strengthen the effectiveness of meshless methods, Oh et al. developed meshfree reproducing polynomial particle (RPP) shape functions, patchwise RPP and reproducing singularity particle (RSP) shape functions with use of flat-top partition of unity. All of these approximation functions satisfy the Kronecker delta property. In this paper, we report that meshfree RPP shape functions, patchwise RPP shape functions, and patchwise RSP shape functions effectively handle boundary integral equations with (or without) domain singularities.