Approaches MPI+OpenMP implementation of conjugated gradient method with pre-conditioner of block incomplete inverse triangular decomposition of IC1

Abstract

The paper considers a preconditioner for solving systems of linear algebraic equations with a symmetric positively defined matrix – a preconditioner of the block incomplete inverse triangular decomposition of the first order "by value" BIIC-IC1. The invention considers a method of using MPI+OpenMP technology for the construction and application of the BIIC-IC1 preconditioner, in which the number of blocks in a preconditioner is multiple the number of processor used and the number of threads used. A new method of using MPI+OpenMP technology for constructing and handling a preconditioner BIIC-IC1 with a number of blocks coinciding with the number of processors is proposed, in which a special ordering of grid nodes inside subareas corresponding to calculations on each processor is used to apply the OpenMP technology. Time of solving problems is compared by method of conjugated gradients with preconditioner BIIC-IC1 using MPI and hybrid MPI+OpenMP technology using example of model problem and number of tasks from collection of sparse matrices SuiteSparse.