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Iterative methods for shifted positive definite linear systems and time discretization of the heat equation

W. Maclean ; Vidar Thomée (Institutionen för matematiska vetenskaper, matematik)

In earlier work we have studied a method for discretization in time of a parabolic problem which consists in 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, and in this paper we study iterative methods for such systems. We first consider the basic and a preconditioned version of the Richardson algorithm, and then a conjugate gradient method as well as a preconditioned version thereof.

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

Denna post skapades 2012-02-27.
CPL Pubid: 155437


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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)


Numerisk analys

Chalmers infrastruktur