Robustness of MILU with respect to
the Coefficients of the PDE
Maria Elizabeth G. Ong
University of California, San Diego
Tony F. Chan
University of California, Los A ngeles
Tarek P. Mathew
University of Wyoming
Preconditioned conjugate gradients is a popular method for solving symmetric
positive definite linear systems; the preconditioner is used to accelerate
convergence. One indicator of the rate of convergence is the condition number
of the preconditioned coefficient matrix. Good preconditioners reduce the
condition number and/or cluster the eigenvalues of the coefficient matrix. In
addition, they should be simple to implement and applicable to a wide class of
problems; that is, they should be robust.
A popular preconditioner is the modified incomplete LU (MILU) factorization.
In this talk, we show the robustness of MILU for problems with anisotropic or
discontinuous coefficients. We demonstrate robustness by showing that the
condition number of the preconditioned coefficient matrix is independent of
the coefficients of the underlying partial differential equation.