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

Details Iterative methods for shifted positive definite linear systems and time discretization of the heat equation Iterative methods for shifted positive definite linear systems and time discretization of the heat equation

2011-11-22

arxiv.org/abs/1111.5105v1

Mathematics

Numerical Analysis

Scientific paper

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.

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