Iterative solution of shifted positive-definite linear systems arising in a numerical method for the heat equation based on Laplace transformation and quadrature
Journal article, 2011

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.

conjugate gradient method

finite elements

Laplace transform

Richardson iteration




William McLean

University of New South Wales (UNSW)

Vidar Thomee

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

ANZIAM Journal

1446-1811 (ISSN)

Vol. 53 2 134-155

Subject Categories

Computational Mathematics


Basic sciences



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