Journal Article

A parallel method for time discretization of parabolic equations based on Laplace transformation and quadrature

Dongwoo Sheen, Ian H. Sloan and Vidar Thomée

in IMA Journal of Numerical Analysis

Published on behalf of Institute of Mathematics and its Applications

Volume 23, issue 2, pages 269-299
Published in print April 2003 | ISSN: 0272-4979
Published online April 2003 | e-ISSN: 1464-3642 | DOI: https://dx.doi.org/10.1093/imanum/23.2.269
A parallel method for time discretization of parabolic equations based on Laplace transformation and quadrature

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We consider the discretization in time of an inhomogeneous parabolic equation in a Banach space setting, using a representation of the solution as an integral along a smooth curve in the complex left half‐plane which, after transformation to a finite interval, is then evaluated to high accuracy by a quadrature rule. This reduces the problem to a finite set of elliptic equations with complex coefficients, which may be solved in parallel. The paper is a further development of earlier work by the authors, where we treated the homogeneous equation in a Hilbert space framework. Special attention is given here to the treatment of the forcing term. The method is combined with finite‐element discretization in spatial variables.

Keywords: parabolic problems; parallel algorithm; Laplace transform; quadrature

Journal Article.  0 words. 

Subjects: Mathematics

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