Stability analysis of method of fundamental solutions for mixed boundary value problems of Laplace’s equation

Computing ◽  
2010 ◽  
Vol 88 (1-2) ◽  
pp. 1-29 ◽  
Author(s):  
Zi-Cai Li ◽  
Jin Huang ◽  
Hung-Tsai Huang
Keyword(s):  
Stability Analysis ◽  
Boundary Value Problems ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Fundamental Solutions ◽  
Method Of Fundamental Solutions ◽  
Laplace’S Equation ◽  
Mixed Boundary Value Problems ◽  
Laplace's Equation

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

2013 ◽  
Vol 11 (8) ◽  
Author(s):  
Csaba Gáspár
Keyword(s):  
Boundary Value Problems ◽  
Radial Basis Functions ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Fundamental Solutions ◽  
Higher Order ◽  
Basis Functions ◽  
Method Of Fundamental Solutions ◽  
Numerical Examples ◽  
Ill Conditioned Matrices

AbstractThe 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.

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