A BLOCK FSAI-ILU PARALLEL PRECONDITIONER FOR SYMMETRIC POSITIVE DEFINITE LINEAR SYSTEMS

作者：Janna Carlo^*; Ferronato Massimilano; Gambolati Giuseppe

来源：SIAM Journal on Scientific Computing, 2010, 32(5): 2468-2484.

DOI：10.1137/090779760

• Krylov subspace methods
• preconditioning
• factorized sparse approximate inverse
• incomplete factorization
• parallel computing

A novel parallel preconditioner for symmetric positive definite matrices is developed coupling a generalized factored sparse approximate inverse (FSAI) with an incomplete LU (ILU) factorization. The generalized FSAI, called block FSAI, is derived by requiring the preconditioned matrix to resemble a block-diagonal matrix in the sense of the minimal Frobenius norm. An incomplete block Jacobi algorithm is then effectively used to accelerate the convergence of a Krylov subspace method. The block FSAI-ILU preconditioner proves superior to both FSAI and the incomplete block Jacobi by themselves in a number of realistic finite element test cases and is fully scalable for a given number of blocks.

• 出版日期2010