Volume 2, Issue 3
An Explicit-Implicit Predictor-Corrector Domain Decomposition Method for Time Dependent Multi-Dimensional Convection Diffusion Equations

Liyong Zhu, Guangwei Yuan & Qiang Du

Numer. Math. Theor. Meth. Appl., 2 (2009), pp. 301-325.

Published online: 2009-02

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  • Abstract

The numerical solution of large scale multi-dimensional convection diffusion equations often requires efficient parallel algorithms. In this work, we consider the extension of a recently proposed non-overlapping domain decomposition method for two dimensional time dependent convection diffusion equations with variable coefficients. By combining predictor-corrector technique, modified upwind differences with explicit-implicit coupling, the method under consideration provides intrinsic parallelism while maintaining good stability and accuracy. Moreover, for multi-dimensional problems, the method can be readily implemented on a multi-processor system and does not have the limitation on the choice of subdomains required by some other similar predictor-corrector or stabilized schemes. These properties of the method are demonstrated in this work through both rigorous mathematical analysis and numerical experiments.

  • Keywords

Convection diffusion equation, parallel algorithm, domain decomposition, modified upwind differences, predictor-corrector, explicit-implicit scheme, convergence analysis.

  • AMS Subject Headings

65N30, 65F10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-2-301, author = {}, title = {An Explicit-Implicit Predictor-Corrector Domain Decomposition Method for Time Dependent Multi-Dimensional Convection Diffusion Equations}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2009}, volume = {2}, number = {3}, pages = {301--325}, abstract = {

The numerical solution of large scale multi-dimensional convection diffusion equations often requires efficient parallel algorithms. In this work, we consider the extension of a recently proposed non-overlapping domain decomposition method for two dimensional time dependent convection diffusion equations with variable coefficients. By combining predictor-corrector technique, modified upwind differences with explicit-implicit coupling, the method under consideration provides intrinsic parallelism while maintaining good stability and accuracy. Moreover, for multi-dimensional problems, the method can be readily implemented on a multi-processor system and does not have the limitation on the choice of subdomains required by some other similar predictor-corrector or stabilized schemes. These properties of the method are demonstrated in this work through both rigorous mathematical analysis and numerical experiments.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2009.m8016}, url = {http://global-sci.org/intro/article_detail/nmtma/6061.html} }
TY - JOUR T1 - An Explicit-Implicit Predictor-Corrector Domain Decomposition Method for Time Dependent Multi-Dimensional Convection Diffusion Equations JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 301 EP - 325 PY - 2009 DA - 2009/02 SN - 2 DO - http://doi.org/10.4208/nmtma.2009.m8016 UR - https://global-sci.org/intro/article_detail/nmtma/6061.html KW - Convection diffusion equation, parallel algorithm, domain decomposition, modified upwind differences, predictor-corrector, explicit-implicit scheme, convergence analysis. AB -

The numerical solution of large scale multi-dimensional convection diffusion equations often requires efficient parallel algorithms. In this work, we consider the extension of a recently proposed non-overlapping domain decomposition method for two dimensional time dependent convection diffusion equations with variable coefficients. By combining predictor-corrector technique, modified upwind differences with explicit-implicit coupling, the method under consideration provides intrinsic parallelism while maintaining good stability and accuracy. Moreover, for multi-dimensional problems, the method can be readily implemented on a multi-processor system and does not have the limitation on the choice of subdomains required by some other similar predictor-corrector or stabilized schemes. These properties of the method are demonstrated in this work through both rigorous mathematical analysis and numerical experiments.

Liyong Zhu, Guangwei Yuan & Qiang Du. (2020). An Explicit-Implicit Predictor-Corrector Domain Decomposition Method for Time Dependent Multi-Dimensional Convection Diffusion Equations. Numerical Mathematics: Theory, Methods and Applications. 2 (3). 301-325. doi:10.4208/nmtma.2009.m8016
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