Iterative methods for shifted positive definite linear systems and time discretization of the heat equation
Preprint, 2011

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.

quadrature

finite elements

conjugate gradient method

Laplace transform

preconditioning.

Richardson iteration

Author

W. Maclean

Vidar Thomee

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Subject Categories

Computational Mathematics

More information

Created

10/6/2017