# Multigrid Becomes a Competitive Algorithm for some 3D Device Simulation Problems

• J. Fuhrmann
• K. Gärtner
Conference paper

## Abstract

For situations where Gummel’s decoupling scheme is applicable a multigrid algorithm for the continuity equations fully consistent with the usual ScharfetterGummel discretization can be used to solve the van Roosbroeck equations. The main problems for applying a multigrid algorithm are that discrete spaces are not nested in the usual sense for the refined grids because of the ScharfetterGummel discretization and that problem coefficients vary strongly. Transforming the equations to symmetric form and applying a block MILU decomposition based on the coarse-fine splitting of the discrete spaces with a perturbed Schur complement defines the prolongation and restriction operators. The transformation back to the original variables is possible. Coarse grid matrices are M-matrices.

## Keywords

Coarse Grid Multigrid Method Domain Decomposition Method Competitive Algorithm Multigrid Algorithm
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