The method of fundamental solutions for potential, Helmholtz and diffusion problems. (English) Zbl 0945.65130

Golberg, M. A.; Chen, C. S.

Golberg, Michael (ed.), Boundary integral methods: numerical and mathematical aspects. Southampton: WIT Press/ Computational Mechanics Publications. Comput Eng. 1, 103-176 (1999).

The authors consider a modified boundary element method in which they represent solutions by use of layer potentials on surfaces which are not the physical ones. In fact they perturb (modify) the domain on which the problems are formulated. Unfortunately, it is not very clear how this perturbation affects the solution of the problem. However, they observe, at least from the numerical point of view, that such perturbations can lead to singular problems (algebraic systems).
For the entire collection see [Zbl 0930.00013].

Reviewer: C.I.Gheorghiu (Cluj-Napoca)

MSC:

65N38	Boundary element methods for boundary value problems involving PDEs
65M70	Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35J05	Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35K05	Heat equation

Keywords:

method of fundamental solutions; Laplace equation; Poisson equation; perturbation; Helmholtz equation; diffusion equations; boundary element method; domains with corners

Software:

LINPACK