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Volume 5, Issue 4
Galerkin Formulations of the Method of Fundamental Solutions

J. R. Berger & Andreas Karageorghis

DOI: 10.4208/aamm.13-13S02

Adv. Appl. Math. Mech., 5 (2013), pp. 423-441.

Published online: 2013-08

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  • Abstract

In this paper, we introduce two Galerkin formulations of the Method of Fundamental Solutions (MFS). In contrast to the collocation formulation of the MFS, the proposed Galerkin formulations involve the evaluation of integrals over the boundary of the domain under consideration. On the other hand, these formulations lead to some desirable properties of the stiffness matrix such as symmetry in certain cases. Several numerical examples are considered by these methods and their various features compared.

  • Keywords

Galerkin formulation, Laplace equation, method of fundamental solutions.

  • AMS Subject Headings

65N38, 65N30, 65N35, 65N80

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-5-423, author = {Berger , J. R. and Karageorghis , Andreas}, title = {Galerkin Formulations of the Method of Fundamental Solutions}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2013}, volume = {5}, number = {4}, pages = {423--441}, abstract = {

In this paper, we introduce two Galerkin formulations of the Method of Fundamental Solutions (MFS). In contrast to the collocation formulation of the MFS, the proposed Galerkin formulations involve the evaluation of integrals over the boundary of the domain under consideration. On the other hand, these formulations lead to some desirable properties of the stiffness matrix such as symmetry in certain cases. Several numerical examples are considered by these methods and their various features compared.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.13-13S02}, url = {http://global-sci.org/intro/article_detail/aamm/78.html} }
TY - JOUR T1 - Galerkin Formulations of the Method of Fundamental Solutions AU - Berger , J. R. AU - Karageorghis , Andreas JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 423 EP - 441 PY - 2013 DA - 2013/08 SN - 5 DO - http://doi.org/10.4208/aamm.13-13S02 UR - https://global-sci.org/intro/article_detail/aamm/78.html KW - Galerkin formulation, Laplace equation, method of fundamental solutions. AB -

In this paper, we introduce two Galerkin formulations of the Method of Fundamental Solutions (MFS). In contrast to the collocation formulation of the MFS, the proposed Galerkin formulations involve the evaluation of integrals over the boundary of the domain under consideration. On the other hand, these formulations lead to some desirable properties of the stiffness matrix such as symmetry in certain cases. Several numerical examples are considered by these methods and their various features compared.

Berger , J. R. and Karageorghis , Andreas. (2013). Galerkin Formulations of the Method of Fundamental Solutions. Advances in Applied Mathematics and Mechanics. 5 (4). 423-441. doi:10.4208/aamm.13-13S02
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