A parallel method

for time-discretization of parabolic problems

based on contour integral representation

and quadrature

Authors:
Dongwoo Sheen, Ian H. Sloan and Vidar Thomée

Journal:
Math. Comp. **69** (2000), 177-195

MSC (1991):
Primary {65M12, 65M15, 65M99}

DOI:
https://doi.org/10.1090/S0025-5718-99-01098-4

Published electronically:
April 7, 1999

MathSciNet review:
1648403

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We treat the time discretization of an initial-value problem for a homogeneous abstract parabolic equation by first using a representation of the solution as an integral along the boundary of a sector in the right half of the complex plane, then transforming this into a real integral on the finite interval , and finally applying a standard quadrature formula to this integral. The method requires the solution of a finite set of elliptic problems with complex coefficients, which are independent and may therefore be done in parallel. The method is combined with spatial discretization by finite elements.

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Additional Information

**Dongwoo Sheen**

Affiliation:
Department of Mathematics, Seoul National University, Seoul 151-742, Korea

Email:
sheen@math.snu.ac.kr

**Ian H. Sloan**

Affiliation:
School of Mathematics, University of New South Wales, Sydney 2052, Australia

Email:
sloan@maths.unsw.edu.au

**Vidar Thomée**

Affiliation:
Department of Mathematics, Chalmers University of Technology, S-412 96 Göte- borg, Sweden

Email:
thomee@math.chalmers.se

DOI:
https://doi.org/10.1090/S0025-5718-99-01098-4

Received by editor(s):
March 26, 1998

Published electronically:
April 7, 1999

Additional Notes:
This work was partially supported by the Australian Research Council and the Korea Science & Engineering Foundation through the Global Analysis Research Center at Seoul National University.

Article copyright:
© Copyright 1999
American Mathematical Society