A Class of Parallel Multilevel Sparse Approximate Inverse Preconditioners for Sparse Linear Systems

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Kai Wang
Jun Zhang
Chi Shen


We investigate the use of the multistep successive preconditioning
strategies (MSP) to construct a class of parallel multilevel
sparse approximate inverse (SAI) preconditioners.
We do not use independent set ordering,
but a diagonal dominance based matrix
permutation to build a multilevel structure.
The purpose of introducing multilevel structure into SAI is
to enhance the robustness of SAI for solving difficult problems.
Forward and backward preconditioning iteration and
two Schur complement preconditioning strategies are proposed to
improve the performance
and to reduce the storage cost of the multilevel preconditioners.
One version of the parallel multilevel SAI preconditioner
based on the MSP strategy
is implemented. Numerical experiments for solving
a few sparse matrices on a distributed memory
parallel computer are reported.

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