A multigrid method for solving the nonlinear diffusion equation on a time-dependent domain using rectangular grids in cartesian coordinates

Using implicit time discretization methods combined with space discretization by finite differences for solving the diffusion equation in VLSI process simulation-leads to large systems of equations that have to be solved at every time-step. For this purpose, a multigrid (MG) algorithm was constructed. Spatial discretization in cartesian coordinates is done in the (non-transformed) physical domain. It is demonstrated that the method of discretization, relaxation and residual transfer used here combined with a nonlinear variant of the MG-method ("Full Approximation Scheme" (FAS)) yields convergence rates of less than or about 0.1, even for extremely large time steps, Further it is estimated that the amount of computational work is about ten percent of that for a single grid method using an explicit time discretization scheme for the problem at hand.