Volume 20, Issue 5
A Conservative Parallel Iteration Scheme for Nonlinear Diffusion Equations on Unstructured Meshes

Yunlong Yu, Yanzhong Yao, Guangwei Yuan & Xingding Chen

Commun. Comput. Phys., 20 (2016), pp. 1405-1423.

Published online: 2018-04

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  • Abstract

In this paper, a conservative parallel iteration scheme is constructed to solve nonlinear diffusion equations on unstructured polygonal meshes. The design is based on two main ingredients: the first is that the parallelized domain decomposition is embedded into the nonlinear iteration; the second is that prediction and correction steps are applied at subdomain interfaces in the parallelized domain decomposition method. A new prediction approach is proposed to obtain an efficient conservative parallel finite volume scheme. The numerical experiments show that our parallel scheme is second-order accurate, unconditionally stable, conservative and has linear parallel speed-up.

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@Article{CiCP-20-1405, author = {}, title = {A Conservative Parallel Iteration Scheme for Nonlinear Diffusion Equations on Unstructured Meshes}, journal = {Communications in Computational Physics}, year = {2018}, volume = {20}, number = {5}, pages = {1405--1423}, abstract = {

In this paper, a conservative parallel iteration scheme is constructed to solve nonlinear diffusion equations on unstructured polygonal meshes. The design is based on two main ingredients: the first is that the parallelized domain decomposition is embedded into the nonlinear iteration; the second is that prediction and correction steps are applied at subdomain interfaces in the parallelized domain decomposition method. A new prediction approach is proposed to obtain an efficient conservative parallel finite volume scheme. The numerical experiments show that our parallel scheme is second-order accurate, unconditionally stable, conservative and has linear parallel speed-up.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.230815.030616a}, url = {http://global-sci.org/intro/article_detail/cicp/11195.html} }
TY - JOUR T1 - A Conservative Parallel Iteration Scheme for Nonlinear Diffusion Equations on Unstructured Meshes JO - Communications in Computational Physics VL - 5 SP - 1405 EP - 1423 PY - 2018 DA - 2018/04 SN - 20 DO - http://doi.org/10.4208/cicp.230815.030616a UR - https://global-sci.org/intro/article_detail/cicp/11195.html KW - AB -

In this paper, a conservative parallel iteration scheme is constructed to solve nonlinear diffusion equations on unstructured polygonal meshes. The design is based on two main ingredients: the first is that the parallelized domain decomposition is embedded into the nonlinear iteration; the second is that prediction and correction steps are applied at subdomain interfaces in the parallelized domain decomposition method. A new prediction approach is proposed to obtain an efficient conservative parallel finite volume scheme. The numerical experiments show that our parallel scheme is second-order accurate, unconditionally stable, conservative and has linear parallel speed-up.

Yunlong Yu, Yanzhong Yao, Guangwei Yuan & Xingding Chen. (2020). A Conservative Parallel Iteration Scheme for Nonlinear Diffusion Equations on Unstructured Meshes. Communications in Computational Physics. 20 (5). 1405-1423. doi:10.4208/cicp.230815.030616a
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