Localized space–time method of fundamental solutions for three-dimensional transient diffusion problem

A localized space–time method of fundamental solutions (LSTMFS) is extended for solving three-dimensional transient diffusion problems in this paper. The interval segmentation in temporal direction is developed for the accurate simulation of long-time-dependent diffusion problems. In the LSTMFS, the whole space–time domain with nodes arranged is divided into a series of overlapping subdomains with a simple geometry. In each subdomain, the conventional method of fundamental solutions is utilized and the coefficients associated with the considered domain can be explicitly determined. By calculating a combined sparse matrix system, the value at any node inside the space–time domain can be obtained. Numerical experiments demonstrate that high accuracy and efficiency can be simultaneously achieved via the LSTMFS, even for the problems defined on a long-time and quite complex computational domain.