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SUMMARYWhen solving parabolic partial differential equations using finite difference non-overlapping domain decomposition methods, one often uses the stripwise decomposition of spatial domain and it can be extended to the rectangular decomposition without further analysis. In this paper, we analyze the rectangular decomposition when the modified implicit prediction (MIP) algorithm is used. We show that the performance of the rectangular decomposition and the stripwise decomposition is different. We compare spectral radius, maximum error, efficiency, and total operations of the rectangular and the stripwise decompositions. We investigate the accuracy of the interface of the rectangular decomposition and the effects of the correction phase of the rectangular decomposition. Numerical experiments have been done in both two and three spatial dimensions and show that the rectangular decomposition is not better than the stripwise decomposition.

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