Iterative methods for shifted positive definite linear systems and time discretization of the heat equation
Numerical Analysis
2016-02-02 v1 Analysis of PDEs
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.
Keywords
Cite
@article{arxiv.1111.5105,
title = {Iterative methods for shifted positive definite linear systems and time discretization of the heat equation},
author = {William McLean and Vidar Thomée},
journal= {arXiv preprint arXiv:1111.5105},
year = {2016}
}