General Framework of Preconditioners

Ernst P. Stephan () and Thanh Tran ()
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Ernst P. Stephan: Leibniz University Hannover
Thanh Tran: The University of New South Wales

Chapter Chapter 2 in Schwarz Methods and Multilevel Preconditioners for Boundary Element Methods, 2021, pp 13-69 from Springer

Abstract: Abstract This chapter provides the general framework of preconditioning by additive and multiplicative Schwarz operators. Preconditioners are viewed from different angles: in the matrix form, variational form, and operator form. We discuss how to implement the preconditioner with the conjugate gradient method, the generalised minimum residual method, and with a linear iterative method. For FEM-BEM coupling problems, we introduce ORTHODIR and the hybrid modified conjugate residual methods, which are Krylov methods. Convergence analysis for all these methods are presented.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-79283-1_2

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DOI: 10.1007/978-3-030-79283-1_2

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