High order projection plane method for evaluation of supersingular curved boundary integrals in BEM
type: Item
instance of: scholarly article
title: High order projection plane method for evaluation of supersingular curved boundary integrals in BEM
zbMATH Open document ID: 1400.74115
DOI: 10.1155/2016/9523405
author: Miao Cui
author: Kai Yang
author: Wei-Zhe Feng
author: Xiaowei Gao
published in: Mathematical Problems in Engineering
publication date: 2018-10-12T00:00:00Z
review text: Summary: Boundary element method (BEM) is a very promising approach for solving various engineering problems, in which accurate evaluation of boundary integrals is required. In the present work, the direct method for evaluating singular curved boundary integrals is developed by considering the third-order derivatives in the projection plane method when expanding the geometry quantities at the field point as Taylor series. New analytical formulas are derived for geometry quantities defined on the curved line/plane, and unified expressions are obtained for both two-dimensional and three-dimensional problems. For the two-dimensional boundary integrals, analytical expressions for the third-order derivatives are derived and are employed to verify the complex-variable-differentiation method (CVDM) which is used to evaluate the high order derivatives for three-dimensional problems. A few numerical examples are given to show the effectiveness and the accuracy of the present method.
Mathematics Subject Classification ID: 74S15
Mathematics Subject Classification ID: 65N38
Mathematics Subject Classification ID: 74S70
zbMATH DE Number: 6953802
Wikidata QID: Q59141288
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/9523405
OpenAlex ID: W2296508586
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description: scientific article; zbMATH DE number 6953802