Stability analysis of the method of fundamental solutions with smooth closed pseudo-boundaries for Laplace's equation: better pseudo-boundaries
The stability analysis of the MFS approximation to the solution of Laplace's equation with Dirichlet boundary conditions for non-circular/non-elliptic pseudo-boundaries is investigated based on new techniques without employing circulant matrices. Bounds of the condition number of the resulting MFS system are derived, whilst exponential growth rates are also obtained. Numerical experiments are carried out to verify the stability analysis performed. Five types of pseudo-boundaries are also proposed in case of singular solutions.
scientific article; zbMATH DE number 7490870
scientific article