A Multigrid Preconditioner for the Semiconductor Equations

نویسندگان

Juan C. Meza

Ray S. Tuminaro

چکیده

A multigrid preconditioned conjugate gradient algorithm is introduced into a semiconductor device modeling code DANCIR This code simulates a wide variety of semiconductor devices by numerically solving the drift di usion equations The most time consuming aspect of the simulation is the solution of three linear systems within each iteration of the Gummel method The original version of DANCIR uses a conjugate gradient iteration preconditioned by an incomplete Cholesky factorization In this paper we consider the replacement of the Cholesky preconditioner by a multigrid preconditioner To adapt the multigrid method to the drift di usion equations interpolation projection and coarse grid discretization operators need to be developed These operators must take into account a number of physical aspects that are present in typical devices wide scale variation in the partial di erential equation PDE coe cients small scale phenomena such as contact points and an oxide layer Additionally suitable relaxation procedures must be designed that give good smoothing numbers in the presence of anisotropic behavior The resulting method is compared with the Cholesky preconditioner on a variety of devices in terms of iterations storage and run time

متن کامل

منابع مشابه

A Black Box Multigrid Preconditioner for Second Order Elliptic Partial Differential Equations

A black box multigrid preconditioner is described for second order elliptic partial differential equations, to be used in pressure calculations in a pressure correction method. The number of cells in each direction is not restricted as for standard multigrid, but completely arbitrary. Fine tuning for cache hits is described. A comparison is made with wall clock times of conventional preconditio...

متن کامل

Krylov Subspace Acceleration for Nonlinear Multigrid Schemes∗

In this paper we present a Krylov acceleration technique for nonlinear PDEs. As a ‘preconditioner’ we use nonlinear multigrid schemes such as the Full Approximation Scheme (FAS) [1]. The benefits of nonlinear multigrid used in combination with the new accelerator are illustrated by difficult nonlinear elliptic scalar problems, such as the Bratu problem, and for systems of nonlinear equations, s...

متن کامل

Chapter 5 Application of Bi - CGSTAB to discretized coupled PDEs

A version of the Bi-CGSTAB method is applied for solving the linear systems that typically occur when applying the Newton method to a discretized set of coupled elliptic partial di erential equations in two dimensions. The Incomplete Line LU decomposition is generalized for the case of coupled equations and applied as a preconditioner. A suitable stopping criterion is developed for the Bi-CGSTA...

متن کامل

A new model of (I+S)-type preconditioner for system of linear equations

In this paper, we design a new model of preconditioner for systems of linear equations. The convergence properties of the proposed methods have been analyzed and compared with the classical methods. Numerical experiments of convection-diffusion equations show a good im- provement on the convergence, and show that the convergence rates of proposed methods are superior to the other modified itera...

متن کامل