Iterative solution of shifted positive-definite linear systems arising in a numerical method for the heat equation based on Laplace transformation and quadrature
Artikel i vetenskaplig tidskrift, 2011

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.

conjugate gradient method

finite elements

Laplace transform

Richardson iteration

quadrature

preconditioning

Författare

William McLean

University of New South Wales (UNSW)

Vidar Thomee

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

ANZIAM Journal

1446-1811 (ISSN)

Vol. 53 2 134-155

Ämneskategorier

Beräkningsmatematik

Fundament

Grundläggande vetenskaper

DOI

10.1017/S1446181112000107