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.