A parallel method for time-discretization of parabolic problems based on contour integral representation and quadrature |
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Authors: | Dongwoo Sheen Ian H Sloan Vidar Thomé e |
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Institution: | Department of Mathematics, Seoul National University, Seoul 151-742, Korea ; School of Mathematics, University of New South Wales, Sydney 2052, Australia ; Department of Mathematics, Chalmers University of Technology, S-412 96 Göteborg, Sweden |
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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 , 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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