arrow
Volume 14, Issue 3
Domain-Decomposition Localized Method of Fundamental Solutions for Large-Scale Heat Conduction in Anisotropic Layered Materials

Shuainan Liu, Zhuojia Fu & Yan Gu

Adv. Appl. Math. Mech., 14 (2022), pp. 759-776.

Published online: 2022-02

Export citation
  • 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.

  • Keywords

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

  • AMS Subject Headings

65N80, 65D25, 35E05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{AAMM-14-759, author = {Liu , ShuainanFu , Zhuojia and Gu , Yan}, title = {Domain-Decomposition Localized Method of Fundamental Solutions for Large-Scale Heat Conduction in Anisotropic Layered Materials}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2022}, volume = {14}, number = {3}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2020-0288}, url = {http://global-sci.org/intro/article_detail/aamm/20283.html} }
TY - JOUR T1 - Domain-Decomposition Localized Method of Fundamental Solutions for Large-Scale Heat Conduction in Anisotropic Layered Materials AU - Liu , Shuainan AU - Fu , Zhuojia AU - Gu , Yan JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 759 EP - 776 PY - 2022 DA - 2022/02 SN - 14 DO - http://doi.org/10.4208/aamm.OA-2020-0288 UR - https://global-sci.org/intro/article_detail/aamm/20283.html KW - Meshless method, localized method of fundamental solutions, heat conduction problems, layered materials, large-scale problems. AB -

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.

Shuainan Liu, Zhuojia Fu & Yan Gu. (2022). Domain-Decomposition Localized Method of Fundamental Solutions for Large-Scale Heat Conduction in Anisotropic Layered Materials. Advances in Applied Mathematics and Mechanics. 14 (3). 759-776. doi:10.4208/aamm.OA-2020-0288
Copy to clipboard
The citation has been copied to your clipboard