Preconditioned CG-type methods for solving the coupled system of fundamental semiconductor equations
This paper presents some experimental results of applying various preconditioned conjugate gradient (CG) type methods to nonsymmetric linear equation systems arising from stationary semiconductor equations. The resultant elliptic BVP is discretized with a rectangular grid with varialble step size determined by the local gradient. The discretized equations are nonlinear, of the form \(F(v)=0\), where v is a block vector. A combimation of a continuation method and a modified Newton method is used to solve these equations, with the applied voltage as continuation parameter. The linearized systems arising from the Newton method are solved by preconditioned generalized CG methods. The authors discuss the construction of a suitable preconditioner and describe two generalized CG methods - GCGLS and CGS [cf. \textit{P. Sonneveld}, SIAM J. Sci. Stat. Comput. 10, 36-52 (1989; Zbl 0666.65029)]. Numerical results using variants of the two methods are presented and compared, together with comparisons with direct Gaussian elimination. The results indicate that a version of GCGLS is likely to be both efficient and robust for solution of the coupled system of 3 nonlinear elliptic boundary value problems describing stationary semiconductor devices.
preconditioned conjugate gradient method
scientific article; zbMATH DE number 4129877
scientific article