MPI+OpenMP IMPLEMENTATION OF CONJUGATE GRADIENT METHOD WITH THE SECOND AND FIRST ORDER INCOMPLETE BLOCK INVERSE TRIANGULAR FACTORIZATION PRECONDITIONERS

O. Yu. Milyukova
VANT. Ser.: Mat. Mod. Fiz. Proc 2022. Вып.1. С. 48-61.

      The paper considers a new preconditioner for solving linear algebraic equation systems with a symmetric positive definite sparse matrix, i.e. a preconditioner for incomplete block inverse triangular factorization of the first order of value. A way of using the (MPI+OpenMP)-process to construct and invert preconditioners for incomplete block inverse triangular decomposition of the second and first order of value is proposed. With the use of the (MPI+OpenMP)-process the number of blocks in such preconditioners is a multiple of the number of processors in use and the number of threads. Comparison is made between the problem runtimes with the use of the MPI process and with the use of the hybrid (MPI+OpenMP)-process for a model problem and for a number of problems from SuiteSparse collection of sparse matrices. The runtime comparison for these problems is performed using the method of conjugate gradients with the second and first order incomplete block inverse triangular factorization preconditioning.