Some variants of the method of fundamental solutions: regularization using radial and nearly radial basis functions

Csaba Gáspár

Open Mathematics (2013)

  • Volume: 11, Issue: 8, page 1429-1440
  • ISSN: 2391-5455

Abstract

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The method of fundamental solutions and some versions applied to mixed boundary value problems are considered. Several strategies are outlined to avoid the problems due to the singularity of the fundamental solutions: the use of higher order fundamental solutions, and the use of nearly fundamental solutions and special fundamental solutions concentrated on lines instead of points. The errors of the approximations as well as the problem of ill-conditioned matrices are illustrated via numerical examples.

How to cite

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Csaba Gáspár. "Some variants of the method of fundamental solutions: regularization using radial and nearly radial basis functions." Open Mathematics 11.8 (2013): 1429-1440. <http://eudml.org/doc/269114>.

@article{CsabaGáspár2013,
abstract = {The method of fundamental solutions and some versions applied to mixed boundary value problems are considered. Several strategies are outlined to avoid the problems due to the singularity of the fundamental solutions: the use of higher order fundamental solutions, and the use of nearly fundamental solutions and special fundamental solutions concentrated on lines instead of points. The errors of the approximations as well as the problem of ill-conditioned matrices are illustrated via numerical examples.},
author = {Csaba Gáspár},
journal = {Open Mathematics},
keywords = {Meshless; Method of fundamental solutions; Regularization; meshless; method of fundamental solutions; regularization; Laplace equation; fourth-order equation; mixed boundary value problems; numerical examples},
language = {eng},
number = {8},
pages = {1429-1440},
title = {Some variants of the method of fundamental solutions: regularization using radial and nearly radial basis functions},
url = {http://eudml.org/doc/269114},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Csaba Gáspár
TI - Some variants of the method of fundamental solutions: regularization using radial and nearly radial basis functions
JO - Open Mathematics
PY - 2013
VL - 11
IS - 8
SP - 1429
EP - 1440
AB - The method of fundamental solutions and some versions applied to mixed boundary value problems are considered. Several strategies are outlined to avoid the problems due to the singularity of the fundamental solutions: the use of higher order fundamental solutions, and the use of nearly fundamental solutions and special fundamental solutions concentrated on lines instead of points. The errors of the approximations as well as the problem of ill-conditioned matrices are illustrated via numerical examples.
LA - eng
KW - Meshless; Method of fundamental solutions; Regularization; meshless; method of fundamental solutions; regularization; Laplace equation; fourth-order equation; mixed boundary value problems; numerical examples
UR - http://eudml.org/doc/269114
ER -

References

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  13. [13] Šarler B., Desingularised method of double layer fundamental solutions for potential flow problems, In: Boundary Elements and Other Mesh Reduction Methods XXX, Maribor, July 7–9, 2008, WIT Trans. Model. Simul., 47, WIT Press, Southampton, 2008, 159–168 
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