Journal
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Volume 33, Issue 6, Pages 3357-3380Publisher
SIAM PUBLICATIONS
DOI: 10.1137/100810368
Keywords
Krylov subspace methods; approximate inverse preconditioning; parallel computing
Categories
Funding
- CINECA
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An adaptive algorithm is presented to generate automatically the nonzero pattern of the block factored sparse approximate inverse (BFSAI) preconditioner. It is demonstrated that in symmetric positive definite (SPD) problems BFSAI minimizes an upper bound to the Kaporin number of the preconditioned matrix. The mathematical structure of this bound suggests an efficient and easily parallelizable strategy for improving the given nonzero pattern of BFSAI, thus providing a novel adaptive BFSAI (ABF) preconditioner. Numerical experiments performed on large sized finite element problems show that ABF coupled with a block incomplete Cholesky (IC) outperforms BFSAI-IC even by a factor of 4, preserving the same preconditioner density and exhibiting an excellent parallelization degree.
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