Gummel-cycle Algebraic Multigrid Preconditioning for Large-scale Device Simulations

It has been proven that the multigrid method is promissing on large-scale scientific simulations. However there still remains some difficulties on applying the multigrid method, which is the system of systems such as FEM on stress analysis or coupled PDEs. Above all, the drift-diffusion model widely used in the device modeling is a typical case belonging to the problems. Because the model has a tight coupling between the electrostatic field and the carrier movements and this property prevents the multigrid method from working effectively. In this paper, we propose a technique to apply the multigrid method to the drift-diffusion model. The technique consists of reflection process between systems coupled in the equation. Consequently the technique helps to solve large-scale device simulations. We show the case of power devices.