Domain-Decomposition Localized Method of Fundamental Solutions for Large-Scale Heat Conduction in Anisotropic Layered Materials (Advances in Applied Mathematics and Mechanics, 2022)
The localized method of fundamental solutions (LMFS) is a relatively newmeshless boundary collocation method. In the LMFS, the global MFS approximation which is expensive to evaluate is replaced by local MFS formulation defined ina set of overlapping subdomains. The LMFS algorithm therefore converts differentialequations 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 adomain-decomposition technique, for the numerical solution of steady-state heat conduction problems in two-dimensional (2D) anisotropic layered materials. Here, thelayered material is decomposed into several subdomains along the layer-layer interfaces, and in each of the subdomains, the solution is approximated by using the LMFSexpansion. On the subdomain interface, compatibility of temperatures and heat fluxesare imposed. Preliminary numerical experiments illustrate that the proposed domain-decomposition LMFS algorithm is accurate, stable and computationally efficient forthe numerical solution of large-scale multi-layered materials.