A parallel method for time discretization of parabolic equations based on Laplace transformation and quadrature |
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Authors: | Sheen Dongwoo; Sloan Ian H; Thomee Vidar |
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Institution: |
1 Department of Mathematics, Seoul National University, 151747, Seoul, Korea 2 School of Mathematics, The University of New South Wales, 2052, Sydney, Australia 3 Department of Mathematics, Chalmers University of Technology, S-412 96, Göteborg, Sweden
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Abstract: | We consider the discretization in time of an inhomogeneous parabolicequation in a Banach space setting, using a representation ofthe solution as an integral along a smooth curve in the complexleft half-plane which, after transformation to a finite interval,is then evaluated to high accuracy by a quadrature rule. Thisreduces the problem to a finite set of elliptic equations withcomplex coefficients, which may be solved in parallel. The paperis a further development of earlier work by the authors, wherewe treated the homogeneous equation in a Hilbert space framework.Special attention is given here to the treatment of the forcingterm. The method is combined with finite-element discretizationin spatial variables. |
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Keywords: | parabolic problems parallel algorithm Laplace transform quadrature |
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