Newton-GMRES Method for Coupled Nonlinear Systems Arising in Semiconductor Device Simulation

Abstract

We are interested in computing the solution of a system of coupled nonlinear PDE’s which describes the electrical behaviour of semiconductor devices. This set of nonlinear equations is solved via a nonlinear version of the GMRES method [2]. This method consists in solving the linear system, that arises in Newton’s method, by an iterative scheme, which constructs an orthonormal basis of a Krylov subspace, and minimizes the residual, over the current Krylov subspace. An advantage of this method over the classical ones is that the Jacobian is not stored and that little storage is required since the method restarts periodically whenever the size of the Krylov subspace reaches a maximum value fixed by the user.