A parallel method for time-discretization of parabolic problems based on contour integral representation and quadrature
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- by Dongwoo Sheen, Ian H. Sloan and Vidar Thomée PDF
- Math. Comp. 69 (2000), 177-195 Request permission
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 $[0,1]$, 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.References
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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
- MR Author ID: 163675
- ORCID: 0000-0003-3769-0538
- Email: sloan@maths.unsw.edu.au
- Vidar Thomée
- Affiliation: Department of Mathematics, Chalmers University of Technology, S-412 96 Göte- borg, Sweden
- MR Author ID: 172250
- Email: thomee@math.chalmers.se
- 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.
- © Copyright 1999 American Mathematical Society
- Journal: Math. Comp. 69 (2000), 177-195
- MSC (1991): Primary {65M12, 65M15, 65M99}
- DOI: https://doi.org/10.1090/S0025-5718-99-01098-4
- MathSciNet review: 1648403