Multigrid approaches to non-linear diffusion problems on unstructured meshes

The e ciency of three multigrid methods for solving highly non-linear di usion problems on two-dimensional unstructured meshes is examined. The three multigrid methods di er 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 all methods are equally e ective at converging the non-linear residual in a given number of grid sweeps, but that the linear solver is more e cient in cpu time due to the lower cost of linear versus non-linear grid sweeps.