Estimation of conflict-free matrix product preconditioner on vector supercomputers

Abstract

Two classes of preconditioners are considered for nonsymmetric linear systems arising from second order difference discretization of non-self-adjoint elliptic partial differential equations. Experimental results show that the usual incomplete LU and modified ILU factorization preconditioner have bad effect due to bank conflict on current vector supercomputers. That is, the bank conflict is an underlying factor for attaining high performance of the vector supercomputers. To avoid the effect of bank conflict, a matrix product preconditioner is introduced. In experiments with two-dimensional problems with constant and variable coefficients on a uniform mesh, the matrix product preconditioner will be shown to be more efficient than the standard incomplete factorization preconditioners.