Multigrid for semiconductor device simulation: cell-centered or vertex-centered multigrid? Math
Jean-michel Molenaar · Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands · 1994
In this paper we study the primal and dual mixed finite element discretization on rectangular grids for the semiconductor device equations.When suitable quadrature rules are used, the primal version is equivalent to the usual vertex-centered box scheme, whereas the dual version leads to a cell-centered finite volume discretization.The systems of nonlinear equations obtained after discretization are solved by the corresponding multigrid methods.In numerical experiments vertex-centered multigrid appears to be more efficient and robust for solving the semiconductor equations than cell-centered multigrid. INTRODUCfiON