Analysis of a two-grid method for semiconductor device problem

doi:10.1007/s10483-021-2696-5

Abstract

Abstract: The mathematical model of a semiconductor device is governed by a system of quasi-linear partial differential equations. The electric potential equation is approximated by a mixed finite element method, and the concentration equations are approximated by a standard Galerkin method. We estimate the error of the numerical solutions in the sense of the L^q norm. To linearize the full discrete scheme of the problem, we present an efficient two-grid method based on the idea of Newton iteration. The main procedures are to solve the small scaled nonlinear equations on the coarse grid and then deal with the linear equations on the fine grid. Error estimation for the two-grid solutions is analyzed in detail. It is shown that this method still achieves asymptotically optimal approximations as long as a mesh size satisfies H=O(h^1/2). Numerical experiments are given to illustrate the efficiency of the two-grid method.

Key words: two-grid method, semiconductor device, mixed finite element method, Galerkin method, L^q error estimate

2010 MSC Number:

35M13
65M12

Ying LIU, Yanping CHEN, Yunqing HUANG, Qingfeng LI. Analysis of a two-grid method for semiconductor device problem. Applied Mathematics and Mechanics (English Edition), 2021, 42(1): 143-158.

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