Efficient implementation of the MFS: The three scenarios
In this study we investigate the approximation of the solutions of harmonic problems subject to Dirichlet boundary conditions by the Method of Fundamental Solutions (MFS). In particular, we study the application of the MFS to Dirichlet problems in a disk. The MFS discretization yields systems which...
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| Published in | Journal of computational and applied mathematics Vol. 227; no. 1; pp. 83 - 92 |
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| Main Authors | , |
| Format | Journal Article Conference Proceeding |
| Language | English |
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Kidlington
Elsevier B.V
01.05.2009
Elsevier |
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| ISSN | 0377-0427 1879-1778 |
| DOI | 10.1016/j.cam.2008.07.010 |
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| Abstract | In this study we investigate the approximation of the solutions of harmonic problems subject to Dirichlet boundary conditions by the Method of Fundamental Solutions (MFS). In particular, we study the application of the MFS to Dirichlet problems in a disk. The MFS discretization yields systems which possess special features which can be exploited by using Fast Fourier transform (FFT)-based techniques. We describe three possible formulations related to the ratio of boundary points to sources, namely, when the number of boundary points is equal, larger and smaller than the number of sources. We also present some numerical experiments and provide an efficient MATLAB implementation of the resulting algorithms. |
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| AbstractList | In this study we investigate the approximation of the solutions of harmonic problems subject to Dirichlet boundary conditions by the Method of Fundamental Solutions (MFS). In particular, we study the application of the MFS to Dirichlet problems in a disk. The MFS discretization yields systems which possess special features which can be exploited by using Fast Fourier transform (FFT)-based techniques. We describe three possible formulations related to the ratio of boundary points to sources, namely, when the number of boundary points is equal, larger and smaller than the number of sources. We also present some numerical experiments and provide an efficient MATLAB implementation of the resulting algorithms. |
| Author | Karageorghis, Andreas Smyrlis, Yiorgos-Sokratis |
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| Cites_doi | 10.1016/j.enganabound.2007.05.004 10.1137/0722040 10.1137/0714043 10.1007/s10543-006-0043-6 10.1023/B:NUMA.0000016581.85429.8d 10.1016/S0955-7997(03)00100-0 10.1090/S0025-5718-09-02191-7 10.1023/A:1018981221740 10.1051/m2an:2004023 10.1007/s10444-004-1833-5 10.1023/A:1012873712701 10.1016/S0955-7997(03)00017-1 10.1002/cnm.537 10.1016/0965-9978(95)00067-4 |
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| Keywords | Least-squares method Method of fundamental solutions Elliptic boundary value problems Variational methods for elliptic equations Over-determined systems Circulant matrices Under-determined systems Fourier transformation Approximation Fast Fourier transformation Fourier analysis Boundary condition Algorithm Partial differential equation Implementation Discretization method Fundamental solution Numerical analysis Elliptic equation Boundary value problem Variational equation Applied mathematics Least squares method Dirichlet problem |
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| SubjectTerms | Calculus of variations and optimal control Circulant matrices Elliptic boundary value problems Exact sciences and technology Least-squares method Mathematical analysis Mathematics Method of fundamental solutions Numerical analysis Numerical analysis. Scientific computation Over-determined systems Partial differential equations Partial differential equations, boundary value problems Sciences and techniques of general use Under-determined systems Variational methods for elliptic equations |
| Title | Efficient implementation of the MFS: The three scenarios |
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