Iterative methods for shifted positive definite linear systems and time discretization of the heat equation
Abstract
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.
 Publication:

arXiv eprints
 Pub Date:
 November 2011
 DOI:
 10.48550/arXiv.1111.5105
 arXiv:
 arXiv:1111.5105
 Bibcode:
 2011arXiv1111.5105M
 Keywords:

 Mathematics  Numerical Analysis;
 Mathematics  Analysis of PDEs;
 65F10;
 65M22;
 65M60;
 65R10
 EPrint:
 ANZIAM J. 53: 134155, 2011