Volume 9, Issue 4
A Time Second-Order Mass-Conserved Implicit-Explicit Domain Decomposition Scheme for Solving the Diffusion Equations

Zhongguo Zhou & Dong Liang

Adv. Appl. Math. Mech., 9 (2017), pp. 795-817.

Published online: 2018-05

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  • Abstract

In the paper, a new time second-order mass-conserved implicit/explicit domain decomposition method (DDM) for the diffusion equations is proposed. In the scheme, firstly, we calculate the interface fluxes of sub-domains from the obtained solutions and fluxes at the previous time level, for which we apply high-order Taylor’s expansion and transfer the time derivatives to spatial derivatives to improve the accuracy. Secondly, the interior solutions and fluxes in sub-domains are computed by the implicit scheme and using the relations between solutions and fluxes, without any correction step. The mass conservation is proved and the convergence order of the numerical solutions is proved to be second-order in both time and space steps. The super-convergence of numerical fluxes is also proved to be second-order in both time and space steps. The scheme is stable under the stable condition r≤3/5. The important feature is that the proposed domain decomposition scheme is mass-conserved and is of second order convergence in time. Numerical experiments confirm the theoretical results.

  • Keywords

Diffusion equations, time second-order, mass-conserved, implicit-explicit domain decomposition, interface fluxes.

  • AMS Subject Headings

65M06, 65M12, 65M55, 76S05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-9-795, author = {}, title = {A Time Second-Order Mass-Conserved Implicit-Explicit Domain Decomposition Scheme for Solving the Diffusion Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {9}, number = {4}, pages = {795--817}, abstract = {

In the paper, a new time second-order mass-conserved implicit/explicit domain decomposition method (DDM) for the diffusion equations is proposed. In the scheme, firstly, we calculate the interface fluxes of sub-domains from the obtained solutions and fluxes at the previous time level, for which we apply high-order Taylor’s expansion and transfer the time derivatives to spatial derivatives to improve the accuracy. Secondly, the interior solutions and fluxes in sub-domains are computed by the implicit scheme and using the relations between solutions and fluxes, without any correction step. The mass conservation is proved and the convergence order of the numerical solutions is proved to be second-order in both time and space steps. The super-convergence of numerical fluxes is also proved to be second-order in both time and space steps. The scheme is stable under the stable condition r≤3/5. The important feature is that the proposed domain decomposition scheme is mass-conserved and is of second order convergence in time. Numerical experiments confirm the theoretical results.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2015.m1049}, url = {http://global-sci.org/intro/article_detail/aamm/12176.html} }
TY - JOUR T1 - A Time Second-Order Mass-Conserved Implicit-Explicit Domain Decomposition Scheme for Solving the Diffusion Equations JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 795 EP - 817 PY - 2018 DA - 2018/05 SN - 9 DO - http://doi.org/10.4208/aamm.2015.m1049 UR - https://global-sci.org/intro/article_detail/aamm/12176.html KW - Diffusion equations, time second-order, mass-conserved, implicit-explicit domain decomposition, interface fluxes. AB -

In the paper, a new time second-order mass-conserved implicit/explicit domain decomposition method (DDM) for the diffusion equations is proposed. In the scheme, firstly, we calculate the interface fluxes of sub-domains from the obtained solutions and fluxes at the previous time level, for which we apply high-order Taylor’s expansion and transfer the time derivatives to spatial derivatives to improve the accuracy. Secondly, the interior solutions and fluxes in sub-domains are computed by the implicit scheme and using the relations between solutions and fluxes, without any correction step. The mass conservation is proved and the convergence order of the numerical solutions is proved to be second-order in both time and space steps. The super-convergence of numerical fluxes is also proved to be second-order in both time and space steps. The scheme is stable under the stable condition r≤3/5. The important feature is that the proposed domain decomposition scheme is mass-conserved and is of second order convergence in time. Numerical experiments confirm the theoretical results.

Zhongguo Zhou & Dong Liang. (2020). A Time Second-Order Mass-Conserved Implicit-Explicit Domain Decomposition Scheme for Solving the Diffusion Equations. Advances in Applied Mathematics and Mechanics. 9 (4). 795-817. doi:10.4208/aamm.2015.m1049
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