Bi-cgstab in Semiconductor Modelling
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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 کاملDelft University of Technology
The Induced Dimension Reduction method [12] was proposed in 1980 as an iterative method for solving large nonsymmetric linear systems of equations. IDR can be considered as the predecessor of methods like CGS (Conjugate Gradient Squared) [9]) and Bi-CGSTAB (Bi-Conjugate Gradients STABilized, [11]). All three methods are based on efficient short recurrences. An important similarity between the m...
متن کاملDELFT UNIVERSITY OF TECHNOLOGY REPORT 08-07 Bi-CGSTAB as an induced dimension reduction method
The Induced Dimension Reduction method [12] was proposed in 1980 as an iterative method for solving large nonsymmetric linear systems of equations. IDR can be considered as the predecessor of methods like CGS (Conjugate Gradient Squared) [9]) and Bi-CGSTAB (Bi-Conjugate Gradients STABilized, [11]). All three methods are based on efficient short recurrences. An important similarity between the m...
متن کاملA Quasi-Minimal Residual Variant of the Bi-CGSTAB Algorithm for Nonsymmetric Systems
Motivated by a recent method of Freund [3], who introduced a quasi-minimal residual (QMR) version of the CGS algorithm, we propose a QMR variant of the Bi-CGSTAB algorithm of van der Vorst, which we call QMRCGSTAB for solving nonsymmetric linear systems. The motivation for both QMR variants is to obtain smoother convergence behavior of the underlying method. We illustrate this by numerical expe...
متن کاملGBi-CGSTAB(s, L): IDR(s) with higher-order stabilization polynomials
IDR(s) is now recognized as one of the most effective methods, often superior to other Krylov subspace methods, for large nonsymmetric linear systems of equations. In this paper we propose an improvement upon IDR(s) by incorporating a higher-order stabilization polynomial into IDR(s). The proposed algorithm, named GBi-CGSTAB(s, L), shares desirable features with both IDR(s) and Bi-CGSTAB(L).
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