A preconditioning strategy for the solution of linear boundary element systems using the GMRES method
type: Item
instance of: scholarly article
title: A preconditioning strategy for the solution of linear boundary element systems using the GMRES method
zbMATH Open document ID: 0880.65009
DOI: 10.1016/S0168-9274(97)00005-6
author: O. Diekmann
published in: Applied Numerical Mathematics
publication date: 1998-02-02T00:00:00Z
review text: The original system is \(Hx=C\) and the authors try to find a nonsingular upper triangular matrix \(A\) such that \(AH= \overline{D}+ \overline{L}+ \overline{V}\), where \(\overline{D}\) and \(\overline{L}\) are diagonal and strictly lower triangular parts of \(AH\) and the purpose is to minimize \(|\overline{V}+ \overline{D}- D|_\infty\) or, in practice, the Frobenius norm \(|\overline{V}+ \overline{D}-D|_F\). This means that the preconditioned system is taken in the form \[ M^{-1}AHx= M^{-1}AC, \qquad M\equiv D+\overline{L}; \] \[ |M^{-1}AH-I|\leq|(I+D^{-1} \overline{L})^{-1}|\cdot|D^{-1}(\overline{V}+ \overline{D}-D)|. \] Numerical experiments associated with the GMRES method are presented; a 20-fold reduction in time was obtained in comparison with the Gauss method for systems with approximately 1300 unknowns.
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65N38
Mathematics Subject Classification ID: 65F35
zbMATH DE Number: 1036643
zbMATH Keywords: preconditioning strategy
zbMATH Keywords: linear boundary element systems
zbMATH Keywords: GMRES method
zbMATH Keywords: numerical examples
zbMATH Keywords: comparison of methods
reviewed by: Evgeniĭ Dyakonov
MaRDI profile type: Publication
cites work: Q4846908
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full work available at URL: s0168-9274(97)00005-6
OpenAlex ID: W2063080991
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description: scientific article; zbMATH DE number 1036643