Publisher： Cambridge University Press
E-ISSN： 1446-8735|53|2|134-155
ISSN： 1446-1811
Source： ANZIAM Journal, Vol.53, Iss.2, 2012-08, pp. : 134-155
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Abstract
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.
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