Analysis of Richardson Iteration in Multigrid Methods for Nonlinear Parabolic Differential Equations

摘要

The behavior of nonlinear Richardson iteration in multigrid methods for solving the implicit relations obtained when an implicit one step method is applied to the space discretized form of a nonlinear parabolic differential equation is analyzed. This analysis leads to an unconventional form of the Richardson method which turns out to be a remarkably efficient predictor formula to start the multigrid method. Numerical experiments are run with a two grid algorithm and a comparison is made with nonlinear Gauss-Seidel iteration. For large integration steps and for strongly nonlinear problems the Richardson iteration method appears to be superior to Gauss-Seidel iteration.