Optimal iterative solvers for linear nonsymmetric systems and nonlinear systems with PDE origins: Balanced black-box stopping tests

Pranjal, Prasad and Silvester, David J. (2018) Optimal iterative solvers for linear nonsymmetric systems and nonlinear systems with PDE origins: Balanced black-box stopping tests. [MIMS Preprint]

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Abstract

This paper discusses the design of efficient algorithms for solving linear nonsymmetric systems and nonlinear systems associated with FEM approximation of elliptic PDEs. The novel feature of the designed linear solvers like GMRES, BICGSTAB(l), TFQMR, and nonlinear solvers like Newton and Picard, is the incorporation of error control in the ‘natural norm’ in combination with an effective a posteriori estimator for the PDE approximation error. This leads to robust and optimal black-box stopping criteria: the iteration is terminated as soon as the algebraic error is insignificant compared to the approximation error.

Item Type:	MIMS Preprint
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User:	professor david silvester
Date Deposited:	13 May 2018 08:49
Last Modified:	13 May 2018 08:49
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/2639

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