The Method of Fundamental Solutions: Theory and Applications /

The Method of Fundamental Solutions: Theory and Applications / / Hung-Tsai HUANG, Yimin WEI, Liping ZHANG, Zi-Cai LI.

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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VerfasserIn:
LI, Zi-Cai,
HUANG, Hung-Tsai,
WEI, Yimin,
Place / Publishing House:Les Ulis : : EDP Sciences, , [2023]
2023
Year of Publication:2023
Language:English
Online Access:
Physical Description:1 online resource (470 p.)
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100 1 |a LI, Zi-Cai,   |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
245 1 4 |a The Method of Fundamental Solutions: Theory and Applications /  |c Hung-Tsai HUANG, Yimin WEI, Liping ZHANG, Zi-Cai LI. 
264 1 |a Les Ulis :   |b EDP Sciences,   |c [2023] 
264 4 |c 2023 
300 |a 1 online resource (470 p.) 
336 |a text  |b txt  |2 rdacontent 
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505 0 0 |t Frontmatter --   |t Contents --   |t Preface --   |t Acknowledgements --   |t Chapter 1. Introduction --   |t Part I. Laplace's Equation --   |t Introduction --   |t CHAPTER 2. Dirichlet Problems --   |t CHAPTER 3. Neumann Problems --   |t CHAPTER 4. Other Boundary Problems --   |t CHAPTER 5. Combined Methods --   |t CHAPTER 6. Source Nodes on Elliptic Pseudo-Boundaries --   |t Part II. Helmholtz's Equations and Other Equations --   |t Introduction --   |t CHAPTER 7. Helmholtz Equations in Simply-Connected Domains --   |t CHAPTER 8. Exterior Problems of Helmholtz Equation --   |t CHAPTER 9. Helmholtz Equations in Bounded Multiply-Connected Domains --   |t CHAPTER 10. Biharmonic Equations --   |t CHAPTER 11. Elastic Problems --   |t CHAPTER 12. Cauchy Problems --   |t CHAPTER 13. 3D Problems --   |t Part III. Selection of Source Nodes and Related Topics --   |t Introduction --   |t CHAPTER 14. Comparisons of MFS and MPS --   |t CHAPTER 15. Stability Analysis for Smooth Closed Pseudo-Boundaries --   |t CHAPTER 16. Singularity Problems from Source Functions; Removal Techniques --   |t CHAPTER 17. Source Nodes on Pseudo Radial-Lines --   |t Epilogue --   |t References --   |t Glossary of Symbols --   |t Index 
506 0 |a restricted access  |u http://purl.org/coar/access_right/c_16ec  |f online access with authorization  |2 star 
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. 
538 |a Mode of access: Internet via World Wide Web. 
546 |a In English. 
588 0 |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 09. Dez 2023) 
650 7 |a MATHEMATICS / Matrices.  |2 bisacsh 
700 1 |a HUANG, Hung-Tsai,   |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
700 1 |a WEI, Yimin,   |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
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