Parabolic Partial Differential Equations

Lehrstuhl füt;r Rechnerstrukturen (IMMD 3)

Universität;t Erlangen-N&uulmt;rnberg

Martensstrasse 3

D-8520 Erlangen

Federal Republic of Germany

Department of Computer Science

Katholieke Universiteit Leuven

Celestijnenlaan 200A

B-3001 Leuven (Heverlee)

Belgium

Mathematical Sciences Section

Oak Ridge National Laboratory

P.O. Box 2008

Oak Ridge, Tennessee 37831-6367

USA

The standard numerical algorithms for solving parabolic partial differential equations are inherently sequential in the time direction. This paper describes an algorithm for the time-accurate solution of certain classes of parabolic partial differential equations that can be parallelized in both time and space. It has a serial complexity that is proportional to the serial complexities of the best known algorithms. The algorithm is a variant of the multigrid waveform relaxation method where the scalar ordinary differential equations that make up the kernel of computation are solved using a cyclic reduction type algorithm. Experimental results obtained on a massively parallel multiprocessor are presented.

Contributed July 30, 1993.