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Iterative solution of shifted positive-definite linear systems arising in a numerical method for the heat equation based on Laplace transformation and quadrature

W. McLean ; Vidar Thomée (Institutionen för matematiska vetenskaper, matematik)
ANZIAM journal (1446-1811). Vol. 53 (2011), 2, p. 134-155.
[Artikel, refereegranskad vetenskaplig]

In earlier work we have studied a method for discretization in time of a parabolic problem, which consists of representing the exact solution as an integral in the complex plane and then applying a quadrature formula to this integral. In application to a spatially semidiscrete finite-element version of the parabolic problem, at each quadrature point one then needs to solve a linear algebraic system having a positive-definite matrix with a complex shift. We study iterative methods for such systems, considering the basic and preconditioned versions of first the Richardson algorithm and then a conjugate gradient method.

Nyckelord: Laplace transform, finite elements, quadrature, Richardson iteration, conjugate gradient method, preconditioning



Denna post skapades 2012-09-08. Senast ändrad 2013-04-09.
CPL Pubid: 163065

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Numerisk analys

Chalmers infrastruktur