The parallel performance of standard parabolic marching schemes

We compare standard parallel algorithms for solving linear parabolic partial differential equations. The comparison is based on the combined effect of their numerical properties and their parallel performance. We discuss the classical explicit methods (forward Euler, Heun and DuFort-Frankel), the standard implicit methods (BDF1, BDF2 and Crank-Nicolson), the line Hopscotch technique and the ADI formula of McKee and Mitchell. Timing results obtained on a 16-processor Intel hypercube are given. It is shown that parallelism does not alter the ranking of the methods unless the number of grid points per processor is very small.status: publishe