ON FIRST ORDER FACTORIZATION METHODS FOR THE SOLUTION OF PROBLEMS WITH MIXED BOUNDARY CONDITIONS AND PROBLEMS WITH DISCONTINUOUS MATERIAL COEFFICIENTS

摘要

In [1] a class of first order factorization methods for the solution of large, sparse systems of equations, of which the coefficient matrix is a symmetric M-matrix, was introduced. Asymptotic results for the computational complexity was proved in the case of systems arising from finite difference approximation of second order self-adjoint elliptic partial differential equation problems in two dimensions with Dirichlet’s boundary conditions, in this paper the result is extended to cover even mixed boundary conditions and problems with discontinuous material coefficients. Results from numerical experiments with various finite difference and finite element approximations are presented and comparisons with direct and other iterative methods are made.