The USC Andrew and Erna Viterbi School of Engineering USC Signal and Image Processing Institute USC Ming Hsieh Department of Electrical Engineering University of Southern California

Technical Report USC-SIPI-162

“A Domain Decomposition Preconditioner Based on a Change to a Multilevel Nodal Basis”

by Charles H. Tong, Tony F. Chan, and C.-C. Jay Kuo

August 1990

We present a domain decomposition method based on a simple change of basis on the interfaces and vertices and we show that this leads to an effective preconditioner compared to the ones previously considered such as the preconditioner by Bramble, Pasciak and Schatz (BPS) [2], and the hierarchical basis domain decomposition (HBDD) preconditioner by Smith and Widlund [8]. Our domain-decomposed preconditioner is based on Bramble, Pasciak and Xu's method give the same order of condition number, namely, O(log2 ) for problems with smooth coefficients. Numerically our method is much more effective and it appears to be O(1) for the model problem.

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