The method of fundamental solutions: theory and applications:
The fundamental solutions (FS) satisfy the governing equations in a solution domain S, and then the numerical solutions can be found from the exterior and the interior boundary conditions on S. The resource nodes of FS are chosen outside S, distinctly from the case of the boundary element method (B...
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Les Ulis
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Les Ulis Science Press [2023] |
| Schriftenreihe: | Current natural sciences
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| Online-Zugang: | DE-1043 DE-1046 DE-858 DE-Aug4 DE-859 DE-860 DE-91 DE-20 DE-706 DE-739 URL des Erstveröffentlichers |
| Zusammenfassung: | The fundamental solutions (FS) satisfy the governing equations in a solution domain S, and then the numerical solutions can be found from the exterior and the interior boundary conditions on S. The resource nodes of FS are chosen outside S, distinctly from the case of the boundary element method (BEM). This method is called the method of fundamental solutions (MFS), which originated from Kupradze in 1963. The Laplace and the Helmholtz equations are studied in detail, and biharmonic equations and the Cauchy-Navier equation of linear elastostatics are also discussed. Moreover, better choices of source nodes are explored. The simplicity of numerical algorithms and high accuracy of numerical solutions are two remarkable advantages of the MFS. However, the ill-conditioning of the MFS is notorious, and the condition number (Cond) grows exponentially via the number of the unknowns used. In this book, the numerical algorithms are introduced and their characteristics are addressed. The main efforts are made to establish the theoretical analysis in errors and stability. The strict analysis (as well as choices of source nodes) in this book has provided the solid theoretical basis of the MFS, to grant it to become an effective and competent numerical method for partial differential equations (PDE). Based on some of our works published as journal papers, this book presents essential and important elements of the MFS. It is intended for researchers, graduated students, university students, computational experts, mathematicians and engineers |
| Beschreibung: | 1 Online-Ressource (xiv, 454 Seiten) |
| ISBN: | 9782759831722 |
| DOI: | 10.1051/978-2-7598-3172-2 |
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| 520 | |a The fundamental solutions (FS) satisfy the governing equations in a solution domain S, and then the numerical solutions can be found from the exterior and the interior boundary conditions on S. The resource nodes of FS are chosen outside S, distinctly from the case of the boundary element method (BEM). This method is called the method of fundamental solutions (MFS), which originated from Kupradze in 1963. The Laplace and the Helmholtz equations are studied in detail, and biharmonic equations and the Cauchy-Navier equation of linear elastostatics are also discussed. Moreover, better choices of source nodes are explored. The simplicity of numerical algorithms and high accuracy of numerical solutions are two remarkable advantages of the MFS. However, the ill-conditioning of the MFS is notorious, and the condition number (Cond) grows exponentially via the number of the unknowns used. In this book, the numerical algorithms are introduced and their characteristics are addressed. The main efforts are made to establish the theoretical analysis in errors and stability. The strict analysis (as well as choices of source nodes) in this book has provided the solid theoretical basis of the MFS, to grant it to become an effective and competent numerical method for partial differential equations (PDE). Based on some of our works published as journal papers, this book presents essential and important elements of the MFS. It is intended for researchers, graduated students, university students, computational experts, mathematicians and engineers | ||
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| illustrated | Not Illustrated |
| index_date | 2024-07-03T23:32:02Z |
| indexdate | 2024-08-21T00:19:46Z |
| institution | BVB |
| isbn | 9782759831722 |
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| spelling | Li, Zi-Cai 1939- Verfasser (DE-588)136187986 aut The method of fundamental solutions: theory and applications Zi-Cai LI, Hung-Tsai HUANG, Yimin WEI and Liping ZHANG Les Ulis EDP Sciences [2023] Les Ulis Science Press [2023] 2023 1 Online-Ressource (xiv, 454 Seiten) txt rdacontent c rdamedia cr rdacarrier Current natural sciences The fundamental solutions (FS) satisfy the governing equations in a solution domain S, and then the numerical solutions can be found from the exterior and the interior boundary conditions on S. The resource nodes of FS are chosen outside S, distinctly from the case of the boundary element method (BEM). This method is called the method of fundamental solutions (MFS), which originated from Kupradze in 1963. The Laplace and the Helmholtz equations are studied in detail, and biharmonic equations and the Cauchy-Navier equation of linear elastostatics are also discussed. Moreover, better choices of source nodes are explored. The simplicity of numerical algorithms and high accuracy of numerical solutions are two remarkable advantages of the MFS. However, the ill-conditioning of the MFS is notorious, and the condition number (Cond) grows exponentially via the number of the unknowns used. In this book, the numerical algorithms are introduced and their characteristics are addressed. The main efforts are made to establish the theoretical analysis in errors and stability. The strict analysis (as well as choices of source nodes) in this book has provided the solid theoretical basis of the MFS, to grant it to become an effective and competent numerical method for partial differential equations (PDE). Based on some of our works published as journal papers, this book presents essential and important elements of the MFS. It is intended for researchers, graduated students, university students, computational experts, mathematicians and engineers MATHEMATICS / Matrices bisacsh Huang, Hung-Tsai Sonstige oth Wei, Yimin Sonstige oth Erscheint auch als Druck-Ausgabe 978-2-7598-3171-5 https://doi.org/10.1051/978-2-7598-3172-2?locatt=mode:legacy Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Li, Zi-Cai 1939- The method of fundamental solutions: theory and applications MATHEMATICS / Matrices bisacsh |
| title | The method of fundamental solutions: theory and applications |
| title_auth | The method of fundamental solutions: theory and applications |
| title_exact_search | The method of fundamental solutions: theory and applications |
| title_exact_search_txtP | The Method of Fundamental Solutions: Theory and Applications |
| title_full | The method of fundamental solutions: theory and applications Zi-Cai LI, Hung-Tsai HUANG, Yimin WEI and Liping ZHANG |
| title_fullStr | The method of fundamental solutions: theory and applications Zi-Cai LI, Hung-Tsai HUANG, Yimin WEI and Liping ZHANG |
| title_full_unstemmed | The method of fundamental solutions: theory and applications Zi-Cai LI, Hung-Tsai HUANG, Yimin WEI and Liping ZHANG |
| title_short | The method of fundamental solutions: theory and applications |
| title_sort | the method of fundamental solutions theory and applications |
| topic | MATHEMATICS / Matrices bisacsh |
| topic_facet | MATHEMATICS / Matrices |
| url | https://doi.org/10.1051/978-2-7598-3172-2?locatt=mode:legacy |
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