A parallel method for time-discretization of parabolic problems based on contour integral representation and quadrature

Sheen, Dongwoo; Sloan, Ian; Thomée, Vidar

doi:10.1090/S0025-5718-99-01098-4

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.

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