Rectangular Domain Decomposition Method for Parabolic Problems
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Abstract
Many partial dierential equations dened on a rectangulardomaincan be solved numericaly by using a domain decomposition me thod. The mostcomonly used ecompositions are the domain being decompos ed in stripwise andrectangular way. Theories for non-overlaping domain decomposition (in whichtwo adjacent subdomains hare an interface) were often focused on the stripwisedecomposition and claimed that extensions could be made to the rectangular de-composition without further discusions. In this paper we focus on the comparisonsof the two ways of decompositions. We consider the unconditionaly stable scheme,the MIP algorithm, for solving parabolic partial dierential equations. The SOR it-erative method is used in the MIP algorithm. Even though the theories are the samebut he performances are dierent. We found out hat he stri pwise decompositionhas beter performance.
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