Multigrid approaches to non‐linear diffusion problems on unstructured meshes

Abstract The efficiency of three multigrid methods for solving highly non‐linear diffusion problems on two‐dimensional unstructured meshes is examined. The three multigrid methods differ mainly in the manner in which the non‐linearities of the governing equations are handled. These comprise a non‐linear full approximation storage (FAS) multigrid method which is used to solve the non‐linear equations directly, a linear multigrid method which is used to solve the linear system arising from a Newton linearization of the non‐linear system, and a hybrid scheme which is based on a non‐linear FAS multigrid scheme, but employs a linear solver on each level as a smoother. Results indicate that, in the asymptotic convergence region, all methods are equally effective at converging the non‐linear residual in a given number of multigrid cycles, but that the linear solver is more efficient in cpu time due to the lower cost of linear versus non‐linear grid sweeps. Copyright © 2001 John Wiley & Sons, Ltd.