Generation of collocation points in the method of fundamental solutions for 2D Laplace's equation

抄録

We propose a new method for generating collocation points that give an accurate approximation in the method of fundamental solutions (MFS). It is known that collocation points that maximize the determinant of the coefficient matrix of the linear system in the MFS give an accurate approximation. However, the maximization problem is intractable. We design an efficient algorithm to automatically take collocation points that do not depend on a boundary condition. Numerical experiments show that the proposed collocation points give a better condition number and an accurate approximation when we use source points far from the boundary.