(untitled) (Advances in Applied Mathematics and Mechanics, 2022)
The localized method of fundamental solutions (LMFS) is a relatively new meshless boundary collocation method. In the LMFS, the global MFS approximation which is expensive to evaluate is replaced by local MFS formulation defined in a set of overlapping subdomains. The LMFS algorithm therefore converts differential equations into sparse rather than dense matrices which are much cheaper to calculate. This paper makes the first attempt to apply the LMFS, in conjunction with a domain-decomposition technique, for the numerical solution of steady-state heat conduction problems in two-dimensional (2D) anisotropic layered materials. Here, the layered material is decomposed into several subdomains along the layer-layer interfaces, and in each of the subdomains, the solution is approximated by using the LMFS expansion. On the subdomain interface, compatibility of temperatures and heat fluxes are imposed. Preliminary numerical experiments illustrate that the proposed domain-decomposition LMFS algorithm is accurate, stable and computationally efficient for the numerical solution of large-scale multi-layered materials.