A novel parallel preconditioner combining a generalized Factored Sparse Approximate Inverse (FSAI) with a block Incomplete LU (ILU) decomposition is developed. The generalized Block FSAI (BFSAI) is derived by requiring the preconditioned matrix to resemble as much as possible a block diagonal matrix in the sense of the minimal Frobenius norm. A second preconditioning is then applied using an incomplete Block Jacobi strategy. The BFSAI-ILU preconditioner turns out to be a parallel hybrid of FSAI and ILU that proves superior to FSAI for any number of processors and is fully scalable for any given number of blocks.
A novel hybrid FSAI-ILU preconditioner for the efficient parallel solution of large size sparse linear systems.
JANNA, CARLO;FERRONATO, MASSIMILIANO;GAMBOLATI, GIUSEPPE
2010
Abstract
A novel parallel preconditioner combining a generalized Factored Sparse Approximate Inverse (FSAI) with a block Incomplete LU (ILU) decomposition is developed. The generalized Block FSAI (BFSAI) is derived by requiring the preconditioned matrix to resemble as much as possible a block diagonal matrix in the sense of the minimal Frobenius norm. A second preconditioning is then applied using an incomplete Block Jacobi strategy. The BFSAI-ILU preconditioner turns out to be a parallel hybrid of FSAI and ILU that proves superior to FSAI for any number of processors and is fully scalable for any given number of blocks.
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