MPI+OpenMP PARALLEL IMPLEMENTATION OF THE CONJUGATE GRADIENT METHOD WITH FACTORIZED EXPLICIT PRECONDITIONINGS
I. E. Kaporin, O. Yu. Milyukova
VANT. Ser.: Mat. Mod. Fiz. Proc 2018. Вып.4. С. 57-69.
For the preconditioning of a symmetric positive definite sparse matrix, its approximate inverse is considered in the form of a product of an upper triangular sparse matrix by its transpose. Several choices of sparsity structure for the preconditioners are considered and analyzed. Parallel implementation of the corresponding linear solvers within the MPI+OpenMP framework is proposed. Comparative timing results are presented based on preconditioned conjugate gradient solution of test problems from the University of Florida sparse matrix collection using MPI, or MPI+OpenMP algorithms. The comparison also includes the point Jacobi preconditioning and the Block Incomplete Inverse preconditioning with the 2nd order Cholesky factorization within the blocks. Keywords: sparse matrices, conjugate gradient method, explicit preconditioning, incomplete inverse triangular factorization, parallel computing.
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