Volume 19, Issue 2
The Mass-Preserving S-DDM Scheme for Two-Dimensional Parabolic Equations

Commun. Comput. Phys., 19 (2016), pp. 411-441.

Published online: 2018-04

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• Abstract

In the paper, we develop and analyze a new mass-preserving splitting domain decomposition method over multiple sub-domains for solving parabolic equations. The domain is divided into non-overlapping multi-bock sub-domains. On the interfaces of sub-domains, the interface fluxes are computed by the semi-implicit (explicit) flux scheme. The solutions and fluxes in the interiors of sub-domains are computed by the splitting one-dimensional implicit solution-flux coupled scheme. The important feature is that the proposed scheme is mass conservative over multiple non-overlapping sub-domains. Analyzing the mass-preserving S-DDM scheme is difficult over non-overlapping multi-block sub-domains due to the combination of the splitting technique and the domain decomposition at each time step. We prove theoretically that our scheme satisfies conservation of mass over multi-block non-overlapping sub-domains and it is unconditionally stable. We further prove the convergence and obtain the error estimate in $L^2$-norm. Numerical experiments confirm theoretical results.

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@Article{CiCP-19-411, author = {}, title = {The Mass-Preserving S-DDM Scheme for Two-Dimensional Parabolic Equations}, journal = {Communications in Computational Physics}, year = {2018}, volume = {19}, number = {2}, pages = {411--441}, abstract = {

In the paper, we develop and analyze a new mass-preserving splitting domain decomposition method over multiple sub-domains for solving parabolic equations. The domain is divided into non-overlapping multi-bock sub-domains. On the interfaces of sub-domains, the interface fluxes are computed by the semi-implicit (explicit) flux scheme. The solutions and fluxes in the interiors of sub-domains are computed by the splitting one-dimensional implicit solution-flux coupled scheme. The important feature is that the proposed scheme is mass conservative over multiple non-overlapping sub-domains. Analyzing the mass-preserving S-DDM scheme is difficult over non-overlapping multi-block sub-domains due to the combination of the splitting technique and the domain decomposition at each time step. We prove theoretically that our scheme satisfies conservation of mass over multi-block non-overlapping sub-domains and it is unconditionally stable. We further prove the convergence and obtain the error estimate in $L^2$-norm. Numerical experiments confirm theoretical results.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.070814.190615a}, url = {http://global-sci.org/intro/article_detail/cicp/11095.html} }
TY - JOUR T1 - The Mass-Preserving S-DDM Scheme for Two-Dimensional Parabolic Equations JO - Communications in Computational Physics VL - 2 SP - 411 EP - 441 PY - 2018 DA - 2018/04 SN - 19 DO - http://doi.org/10.4208/cicp.070814.190615a UR - https://global-sci.org/intro/article_detail/cicp/11095.html KW - AB -

In the paper, we develop and analyze a new mass-preserving splitting domain decomposition method over multiple sub-domains for solving parabolic equations. The domain is divided into non-overlapping multi-bock sub-domains. On the interfaces of sub-domains, the interface fluxes are computed by the semi-implicit (explicit) flux scheme. The solutions and fluxes in the interiors of sub-domains are computed by the splitting one-dimensional implicit solution-flux coupled scheme. The important feature is that the proposed scheme is mass conservative over multiple non-overlapping sub-domains. Analyzing the mass-preserving S-DDM scheme is difficult over non-overlapping multi-block sub-domains due to the combination of the splitting technique and the domain decomposition at each time step. We prove theoretically that our scheme satisfies conservation of mass over multi-block non-overlapping sub-domains and it is unconditionally stable. We further prove the convergence and obtain the error estimate in $L^2$-norm. Numerical experiments confirm theoretical results.

Zhongguo Zhou & Dong Liang. (2020). The Mass-Preserving S-DDM Scheme for Two-Dimensional Parabolic Equations. Communications in Computational Physics. 19 (2). 411-441. doi:10.4208/cicp.070814.190615a
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