SIAM Journal on Scientific Computing vol:16 issue:3 pages:531-541
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.