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An adaptive multilevel factorized sparse approximate inverse preconditioning
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DOI：10.1016/j.advengsoft.2016.10.005.png)
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Abstract
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This paper deals with adaptively preconditioned iterative methods for solving large and sparse systems of linear equations. In particular, the paper discusses preconditioning where adaptive dropping reflects the quality of preserving the relation UZ = I between the direct factor U and the inverse factor Z that satisfy A = (UU)-U-T and A(-1) = ZZ(T). The proposed strategy significantly extends and refines the approach from [1], see also [2], by using a specific multilevel framework. Numerical experiments with two levels demonstrate that the new preconditioning strategy is very promising. Namely, we show a surprising fact that in our approach the Schur complement is better to form in a more sophisticated way than by a standard sparse matrix-matrix multiplication. (C) 2016 Civil-Comp Ltd. and Elsevier Ltd. All rights reserved.
Keywords:
Approximate inverse
Gram-Schmidt orthogonalization
Incomplete factorization
Multilevel methods
Preconditioned conjugate gradient method
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