Numer. Math. Theor. Meth. Appl., 2 (2009), pp. 301-325.
Published online: 2009-02
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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} }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.