An adaptive multilevel factorized sparse approximate inverse preconditioning

作者：Kopal Jiri^*; Rozloznik Miroslav; Tuma Miroslav

来源：Advances in Engineering Software, 2017, 113: 19-24.

DOI：10.1016/j.advengsoft.2016.10.005

• Approximate inverse
• Gram-Schmidt orthogonalization
• Incomplete factorization
• Multilevel methods
• Preconditioned conjugate gradient method

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.

• 出版日期2017-11