An Incomplete Factorization Preconditioning Method for Fem-discretized Partial Diierential Equations Based on Modiication of Element Matrices

It is well known that standard incomplete factorization (IC) methods exist for M-matrices 14] and that modiied incomplete factorization (MIC) methods exist for weakly diagonally dominant matrices 8]. The restriction to these classes of matrices excludes many realistic general applications to discretized partial diieren-tial equations. We present a technique to avoid this problem by making an initial modiication already at the element level, followed by the standard IC or MIC fac-torization of the assembled matrix. This modiication ensures weakly diagonally dominant M-matrices and is made in such a way that the condition number of the matrix is only increased by a constant factor independent of the mesh parameter h. Hence, the fast convergence of the MICCG method, that is in O(h ?1=2); h ! 0 iterations for second order elliptic problems, is preserved.