Preconditioned CG-type methods for solving the coupled system of fundamental semiconductor equations
type: Item
instance of: scholarly article
title: Preconditioned CG-type methods for solving the coupled system of fundamental semiconductor equations
zbMATH Open document ID: 0689.65013
DOI: 10.1007/BF01932752
author: J. M. C. Aarden
author: K.-E. Karlsson
published in: BIT
publication date: 1989-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65Z05
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 78A55
zbMATH DE Number: 4129877
zbMATH Keywords: preconditioned conjugate gradient method
zbMATH Keywords: experimental results
zbMATH Keywords: nonsymmetric linear equation systems
zbMATH Keywords: stationary semiconductor equations
zbMATH Keywords: continuation method
zbMATH Keywords: Newton method
zbMATH Keywords: Numerical results
zbMATH Keywords: comparisons
zbMATH Keywords: Gaussian elimination
describes a project that uses: CGS
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01932752
OpenAlex ID: W2039151860
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description: scientific article; zbMATH DE number 4129877