Adaptive multigrid methods for the simulation of semiconductor devices

Modeling of semiconductor devices leads to a nonlinear singular perturbed system of partial differential equations. Application of multigrid methods for the numerical solution of these equations seems very attractive, but careful modifications and extensions are necessary to ensure the robustness and to achieve typical multigrid efficiency. This talk summarizes the multigrid methods, which have been implemented into the software system MAGIC for the 2-D simulation of arbitrary semiconductor devices. The following topics are considered: -Modified full approximation scheme and its components, -Nested iteration principles for initialization of fine grid solution, - Modification of grid hierarchy and inter-grid transfers to handle small layers on coarse grids, - Adaptive local refinement strategies based on truncation error approximation. Computed results for several examples are presented and efficiency of calculation is compared to standard single grid methods.