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Corrected explicit-implicit domain decomposition algorithms for two-dimensional semilinear parabolic equations

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Abstract

Corrected explicit-implicit domain decomposition (CEIDD) algorithms are studied for parallel approximation of semilinear parabolic problems on distributed memory processors. It is natural to divide the spatial domain into some smaller parallel strips and cells using the simplest straight-line interface (SI). By using the Leray-Schauder fixed-point theorem and the discrete energy method, it is shown that the resulting CEIDD-SI algorithm is uniquely solvable, unconditionally stable and convergent. The CEIDD-SI method always suffers from the globalization of data communication when interior boundaries cross into each other inside the domain. To overcome this disadvantage, a composite interface (CI) that consists of straight segments and zigzag fractions is suggested. The corresponding CEIDD-CI algorithm is proven to be solvable, stable and convergent. Numerical experiments are presented to support the theoretical results.

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Authors and Affiliations

  1. Department of Mathematics, Southeast University, Nanjing, 210096, China

    HongLin Liao & ZhiZhong Sun

  2. Department of Applied Mathematics and Physics, Institute of Sciences, PLAUST, Nanjing, 211101, China

    HongLin Liao & HanSheng Shi

Authors
  1. HongLin Liao
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  2. HanSheng Shi
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  3. ZhiZhong Sun
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Corresponding author

Correspondence to HongLin Liao.

Additional information

This work was supported by National Natural Science Foundation of China (Grant No. 10871044)

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Liao, H., Shi, H. & Sun, Z. Corrected explicit-implicit domain decomposition algorithms for two-dimensional semilinear parabolic equations. Sci. China Ser. A-Math. 52, 2362–2388 (2009). https://doi.org/10.1007/s11425-009-0040-8

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  • DOI: https://doi.org/10.1007/s11425-009-0040-8

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