Domain-Decomposition Localized Method of Fundamental Solutions for Large-Scale Heat Conduction in Anisotropic Layered Materials

Domain-Decomposition Localized Method of Fundamental Solutions for Large-Scale Heat Conduction in Anisotropic Layered Materials

Year:    2022

Author:    Shuainan Liu, Zhuojia Fu, Yan Gu

Advances in Applied Mathematics and Mechanics, Vol. 14 (2022), Iss. 3 : pp. 759–776

Abstract

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2020-0288

Advances in Applied Mathematics and Mechanics, Vol. 14 (2022), Iss. 3 : pp. 759–776

Published online:    2022-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    18

Keywords:    Meshless method localized method of fundamental solutions heat conduction problems layered materials large-scale problems.

Author Details

Shuainan Liu

Zhuojia Fu

Yan Gu