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Domain decomposition for singular perturbation PDEs

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  • Li, Peiyuan
  • Peskin, Richard L.

Abstract

Based on singular perturbation analysis of nonlinear PDEs, we can get an approximate solution of the equation, constructed from a solution of the reduced equation associated with the given nonlinear PDE, and correction terms corresponding to boundary layers and interior layers. By applying the above methods a set of rules to determine a stable partition of a domain can be built. Based on the set of rules the search for all possible stable partitions is implemented by a production system which travels a graph of a given domain. In this paper only elliptic equations are discussed.

Suggested Citation

  • Li, Peiyuan & Peskin, Richard L., 1994. "Domain decomposition for singular perturbation PDEs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 36(4), pages 443-455.
    • Handle: RePEc:eee:matcom:v:36:y:1994:i:4:p:443-455
    DOI: 10.1016/0378-4754(94)90077-9
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    1. Li, Peiyuan & Peskin, Richard L., 1994. "A new search method for domain decomposition for ODEs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 36(4), pages 457-466.
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