MPI+OpenMP Implementation of the Conjugated Gradient Method with Factorized Implicit Preconditioners
O. Yu. Milyukova · Mathematical Models and Computer Simulations · 2022
Abstract Noniterative methods are proposed for using the MPI+OpenMP technology to construct and invert block Jacobi (BJ) preconditioners in combination with an incomplete triangular decomposition with a cutoff in the first order parameter IC1 and a stabilized incomplete triangular decomposition with a cutoff in the second order parameter IC2S. In this case, the number of blocks in the BJ is a multiple of the number of processors used and the number of threads used. Estimates are obtained for the number of iterations of the conjugate gradient (CG) method with BJ preconditioning combined with IC1 or IC2S. Using the calculations of model problems and a number of problems from the collection of sparse matrices SuiteSparse, it is shown that the use of MPI+OpenMP technology can significantly speed up calculations compared to using only MPI for a supercomputer system in which the number of nodes is not excessively large.