Volume 29, Issue 3
Galerkin Boundary Node Method for Exterior Neumann Problems

J. Comp. Math., 29 (2011), pp. 243-260.

Published online: 2011-06

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• Abstract

In this paper, we present a meshless Galerkin scheme of boundary integral equations (BIEs), known as the Galerkin boundary node method (GBNM), for two-dimensional exterior Neumann problems that combines the moving least-squares (MLS) approximations and a variational formulation of BIEs. In this approach, boundary conditions can be implemented directly despite the MLS approximations lack the delta function property. Besides, the GBNM keeps the symmetry and positive definiteness of the variational problems. A rigorous error analysis and convergence study of the method is presented in Sobolev spaces. Numerical examples are also given to illustrate the capability of the method.

• Keywords

Meshless, Galerkin boundary node method, Boundary integral equations, Moving least-squares, Error estimate

65N12, 65N30, 65N38.

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@Article{JCM-29-243, author = {}, title = {Galerkin Boundary Node Method for Exterior Neumann Problems}, journal = {Journal of Computational Mathematics}, year = {2011}, volume = {29}, number = {3}, pages = {243--260}, abstract = {

In this paper, we present a meshless Galerkin scheme of boundary integral equations (BIEs), known as the Galerkin boundary node method (GBNM), for two-dimensional exterior Neumann problems that combines the moving least-squares (MLS) approximations and a variational formulation of BIEs. In this approach, boundary conditions can be implemented directly despite the MLS approximations lack the delta function property. Besides, the GBNM keeps the symmetry and positive definiteness of the variational problems. A rigorous error analysis and convergence study of the method is presented in Sobolev spaces. Numerical examples are also given to illustrate the capability of the method.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1010-m3069}, url = {http://global-sci.org/intro/article_detail/jcm/8477.html} }
TY - JOUR T1 - Galerkin Boundary Node Method for Exterior Neumann Problems JO - Journal of Computational Mathematics VL - 3 SP - 243 EP - 260 PY - 2011 DA - 2011/06 SN - 29 DO - http://doi.org/10.4208/jcm.1010-m3069 UR - https://global-sci.org/intro/article_detail/jcm/8477.html KW - Meshless, Galerkin boundary node method, Boundary integral equations, Moving least-squares, Error estimate AB -

In this paper, we present a meshless Galerkin scheme of boundary integral equations (BIEs), known as the Galerkin boundary node method (GBNM), for two-dimensional exterior Neumann problems that combines the moving least-squares (MLS) approximations and a variational formulation of BIEs. In this approach, boundary conditions can be implemented directly despite the MLS approximations lack the delta function property. Besides, the GBNM keeps the symmetry and positive definiteness of the variational problems. A rigorous error analysis and convergence study of the method is presented in Sobolev spaces. Numerical examples are also given to illustrate the capability of the method.

Xiaolin Li & Jialin Zhu. (1970). Galerkin Boundary Node Method for Exterior Neumann Problems. Journal of Computational Mathematics. 29 (3). 243-260. doi:10.4208/jcm.1010-m3069
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