Some comments on the ill-conditioning of the method of fundamental solutions
In this paper, we consider the accuracy and stability of implementing the method of fundamental solutions. In contrast to the results shown in [5], we find that Gaussian elimination can be used reliably to solve the MFS equations and the use of the singular value decomposition shows no improvement o...
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| Published in | Engineering analysis with boundary elements Vol. 30; no. 5; pp. 405 - 410 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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Oxford
Elsevier Ltd
01.05.2006
Elsevier |
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| Abstract | In this paper, we consider the accuracy and stability of implementing the method of fundamental solutions. In contrast to the results shown in [5], we find that Gaussian elimination can be used reliably to solve the MFS equations and the use of the singular value decomposition shows no improvement over Gaussian elimination provided that the boundary condition is non-noisy. However, for noisy boundary conditions, there is evidence that the singular value decomposition with truncation is more accurate than Gaussian elimination. |
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| AbstractList | In this paper, we consider the accuracy and stability of implementing the method of fundamental solutions. In contrast to the results shown in [5], we find that Gaussian elimination can be used reliably to solve the MFS equations and the use of the singular value decomposition shows no improvement over Gaussian elimination provided that the boundary condition is non-noisy. However, for noisy boundary conditions, there is evidence that the singular value decomposition with truncation is more accurate than Gaussian elimination. |
| Author | Cho, Hokwon A. Chen, C.S. Golberg, M.A. |
| Author_xml | – sequence: 1 givenname: C.S. surname: Chen fullname: Chen, C.S. email: cs.chen@usm.edu organization: Department of Mathematics, University of Southern Mississippi, Hattiesburg, MS 39406, USA – sequence: 2 givenname: Hokwon A. surname: Cho fullname: Cho, Hokwon A. organization: Department of Mathematical Sciences, University of Nevada, Las Vegas, NV 89154, USA – sequence: 3 givenname: M.A. surname: Golberg fullname: Golberg, M.A. organization: 5208 Wilbur St, Las Vegas, NV 89119, USA |
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| Cites_doi | 10.1006/jcph.1998.6178 10.1137/0722040 10.1007/BF03167903 10.1137/1034115 10.1002/cnm.537 10.1137/0914086 10.1023/A:1018981221740 10.1016/0041-5553(64)90006-0 10.1216/JIE-1988-1-4-517 |
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| Keywords | Ill-conditioning Method of fundamental solutions Singular value decomposition Modelling Truncation |
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Karageorghis – volume: 37 start-page: 635 year: 1990 end-page: 657 ident: bib9 article-title: Asymptotic error analysis of the charge simulation method in Jordan regions with an analytic boundary publication-title: J Fac Sci Univ Tokyo Sect 1A Math contributor: fullname: Katsurada – volume: 6 start-page: 253 year: 2005 end-page: 262 ident: bib15 article-title: A meshless method for the Laplace and biharmonic equations subjected to noisy boundary data publication-title: CMES contributor: fullname: Jin – volume: 7 start-page: 119 year: 2004 end-page: 132 ident: bib14 article-title: The method of fundamental solutions for solving multidimensional inverse heat conduction problems publication-title: CMES contributor: fullname: Wei – volume: 34 start-page: 561 year: 1992 end-page: 580 ident: bib11 article-title: Analysis of discrete ill-posed problems by means of the publication-title: SIAM Rev contributor: fullname: Hansen – volume: 14 start-page: 1487 year: 1993 end-page: 1503 ident: bib12 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fullname: Golberg – volume: 37 start-page: 635 year: 1990 ident: 10.1016/j.enganabound.2006.01.001_bib9 article-title: Asymptotic error analysis of the charge simulation method in Jordan regions with an analytic boundary publication-title: J Fac Sci Univ Tokyo Sect 1A Math contributor: fullname: Katsurada – volume: 14 start-page: 1487 year: 1993 ident: 10.1016/j.enganabound.2006.01.001_bib12 article-title: The use of the L-curve in the regularization of discrete ill-posed problems publication-title: SIAM J Sci Comput doi: 10.1137/0914086 contributor: fullname: Hansen – volume: 1 start-page: 1 year: 2004 ident: 10.1016/j.enganabound.2006.01.001_bib1 article-title: Trefftz methods for time dependent partial differential equations publication-title: CMC contributor: fullname: Cho – volume: 9 start-page: 69 year: 1998 ident: 10.1016/j.enganabound.2006.01.001_bib2 article-title: The method of fundamental solution for elliptic boundary value problems publication-title: Adv Comput Math doi: 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| SubjectTerms | Accuracy Boundary conditions Boundary element method Boundary-integral methods Computational techniques Decomposition Exact sciences and technology Fundamental areas of phenomenology (including applications) Gaussian elimination Ill-conditioning Mathematical analysis Mathematical methods in physics Method of fundamental solutions Physics Singular value decomposition Stability |
| Title | Some comments on the ill-conditioning of the method of fundamental solutions |
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