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

We treat the time discretization of an initial-value problem for a ous 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.

• Type: Journal
• Year: 2000
• Where: MOC
• Authors: Dongwoo Sheen, Ian H. Sloan, Vidar Thomée
• Keywords: Abstract Parabolic Equation, Integral, MOC 2000, Time Discretization