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Volume 31, Issue 4
Evaluation of Singular and Nearly Singular Integrals in the BEM with Exact Geometrical Representation

Yaoming Zhang, Wenzhen Qu & Yan Gu

J. Comp. Math., 31 (2013), pp. 355-369.

Published online: 2013-08

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  • Abstract

The geometries of many problems of practical interest are created from circular or elliptic arcs. Arc boundary elements can represent these boundaries exactly, and consequently, errors caused by representing such geometries using polynomial shape functions can be removed. To fully utilize the geometry of circular boundary, the non-singular boundary integral equations (BIEs) and a general nonlinear transformation technique available for arc elements are introduced to remove or damp out the singular or nearly singular properties of the integral kernels. Several benchmark 2D elastostatic problems demonstrate that the present algorithm can effectively handle singular and nearly singular integrals occurring in the boundary element method (BEM) for boundary layer effect and thin-walled structural problems. Owing to the employment of exact geometrical representation, only a small number of elements need to be divided along the boundary and high accuracy can be achieved without increasing other more computational efforts.

  • Keywords

BEM, Singular integrals, Nearly singular integrals, Boundary layer effect, Thin walled structures, Exact geometrical representation.

  • AMS Subject Headings

68Q05.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-31-355, author = {}, title = {Evaluation of Singular and Nearly Singular Integrals in the BEM with Exact Geometrical Representation}, journal = {Journal of Computational Mathematics}, year = {2013}, volume = {31}, number = {4}, pages = {355--369}, abstract = {

The geometries of many problems of practical interest are created from circular or elliptic arcs. Arc boundary elements can represent these boundaries exactly, and consequently, errors caused by representing such geometries using polynomial shape functions can be removed. To fully utilize the geometry of circular boundary, the non-singular boundary integral equations (BIEs) and a general nonlinear transformation technique available for arc elements are introduced to remove or damp out the singular or nearly singular properties of the integral kernels. Several benchmark 2D elastostatic problems demonstrate that the present algorithm can effectively handle singular and nearly singular integrals occurring in the boundary element method (BEM) for boundary layer effect and thin-walled structural problems. Owing to the employment of exact geometrical representation, only a small number of elements need to be divided along the boundary and high accuracy can be achieved without increasing other more computational efforts.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1301-m4021}, url = {http://global-sci.org/intro/article_detail/jcm/9740.html} }
TY - JOUR T1 - Evaluation of Singular and Nearly Singular Integrals in the BEM with Exact Geometrical Representation JO - Journal of Computational Mathematics VL - 4 SP - 355 EP - 369 PY - 2013 DA - 2013/08 SN - 31 DO - http://doi.org/10.4208/jcm.1301-m4021 UR - https://global-sci.org/intro/article_detail/jcm/9740.html KW - BEM, Singular integrals, Nearly singular integrals, Boundary layer effect, Thin walled structures, Exact geometrical representation. AB -

The geometries of many problems of practical interest are created from circular or elliptic arcs. Arc boundary elements can represent these boundaries exactly, and consequently, errors caused by representing such geometries using polynomial shape functions can be removed. To fully utilize the geometry of circular boundary, the non-singular boundary integral equations (BIEs) and a general nonlinear transformation technique available for arc elements are introduced to remove or damp out the singular or nearly singular properties of the integral kernels. Several benchmark 2D elastostatic problems demonstrate that the present algorithm can effectively handle singular and nearly singular integrals occurring in the boundary element method (BEM) for boundary layer effect and thin-walled structural problems. Owing to the employment of exact geometrical representation, only a small number of elements need to be divided along the boundary and high accuracy can be achieved without increasing other more computational efforts.

Yaoming Zhang, Wenzhen Qu & Yan Gu. (1970). Evaluation of Singular and Nearly Singular Integrals in the BEM with Exact Geometrical Representation. Journal of Computational Mathematics. 31 (4). 355-369. doi:10.4208/jcm.1301-m4021
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