The numerical solution of the diffusion equation in VLSI process simulation leads to large systems of nonlinear equations which have to be solved at every time step. For this purpose, a multigrid (MG) algorithm with locally refined grids is constructed. It is demonstrated that the method used here yields typical MG algorithm convergence rates, and reduces the amount of work considerably. The local refinements are controlled by an estimation of the discretization error which is calculated within the nonlinear MG method (FAS) and requires no extra computational work.
Joppich, W. (1991), "A MULTIGRID ALGORITHM WITH TIME‐DEPENDENT, LOCALLY REFINED GRIDS FOR SOLVING THE NONLINEAR DIFFUSION EQUATION ON A NONRECTANGULAR GEOMETRY ‐ PRACTICAL ASPECTS", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 10 No. 4, pp. 411-423. https://doi.org/10.1108/eb051717
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