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A parallel method for time-discretization of parabolic problems based on contour integral representation and quadrature
Author(s):
Dongwoo
Sheen;
Ian
H.
Sloan;
Vidar
Thomée.
Journal:
Math. Comp.
69
(2000),
177-195.
MSC (1991):
Primary {65M12, 65M15, 65M99}
Posted:
April 7, 1999
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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 ![$[0,1]$](/mcom/2000-69-229/S0025-5718-99-01098-4/gif-abstract/img14.gif) , 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 Göteborg, Sweden
Email:
thomee@math.chalmers.se
DOI:
10.1090/S0025-5718-99-01098-4
PII:
S 0025-5718(99)01098-4
Received by editor(s):
March 26, 1998
Posted:
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.
Copyright of article:
Copyright
1999,
American Mathematical Society
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