Volume 1, Issue 4
A Practical Algorithm for Determining the Optimal Pseudo-Boundary in the Method of Fundamental Solutions

A. Karageorghis

Adv. Appl. Math. Mech., 1 (2009), pp. 510-528.

Published online: 2009-01

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  • Abstract

One of the main difficulties in the application of the method of fundamental solutions (MFS) is the determination of the position of the pseudo-boundary on which are placed the singularities in terms of which the approximation is expressed. In this work, we propose a simple practical algorithm for determining an estimate of the pseudo-boundary which yields the most accurate MFS approximation when the method is applied to certain boundary value problems. Several numerical examples are provided.

  • Keywords

Method of fundamental solutions elliptic boundary value problems function minimization

  • AMS Subject Headings

65N35 65N38 65K10

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COPYRIGHT: © Global Science Press

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@Article{AAMM-1-510, author = {A. Karageorghis}, title = {A Practical Algorithm for Determining the Optimal Pseudo-Boundary in the Method of Fundamental Solutions}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2009}, volume = {1}, number = {4}, pages = {510--528}, abstract = {

One of the main difficulties in the application of the method of fundamental solutions (MFS) is the determination of the position of the pseudo-boundary on which are placed the singularities in terms of which the approximation is expressed. In this work, we propose a simple practical algorithm for determining an estimate of the pseudo-boundary which yields the most accurate MFS approximation when the method is applied to certain boundary value problems. Several numerical examples are provided.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.09-m0916}, url = {http://global-sci.org/intro/article_detail/aamm/8383.html} }
TY - JOUR T1 - A Practical Algorithm for Determining the Optimal Pseudo-Boundary in the Method of Fundamental Solutions AU - A. Karageorghis JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 510 EP - 528 PY - 2009 DA - 2009/01 SN - 1 DO - http://doi.org/10.4208/aamm.09-m0916 UR - https://global-sci.org/intro/article_detail/aamm/8383.html KW - Method of fundamental solutions KW - elliptic boundary value problems KW - function minimization AB -

One of the main difficulties in the application of the method of fundamental solutions (MFS) is the determination of the position of the pseudo-boundary on which are placed the singularities in terms of which the approximation is expressed. In this work, we propose a simple practical algorithm for determining an estimate of the pseudo-boundary which yields the most accurate MFS approximation when the method is applied to certain boundary value problems. Several numerical examples are provided.

A. Karageorghis. (1970). A Practical Algorithm for Determining the Optimal Pseudo-Boundary in the Method of Fundamental Solutions. Advances in Applied Mathematics and Mechanics. 1 (4). 510-528. doi:10.4208/aamm.09-m0916
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