Space-time Concurrent Multigrid Waveform Relaxation

Multigrid waveform relaxation is an algorithm for solving parabolic partial differential equations on multicomputers. It is shown in this pa.per that the algorithm allows a. partitioning of the computational domain into space-time blocks, i.e., subdo­ mains of the space-time grid that a.re treated concurrently by different processors. The space-time concurrent multigrid waveform relaxation method is compared to two meth­ ods that use spatial concurrency only: space-concurrent multigrid waveform relaxation and standard time-stepping. It is illustrated that the use of space-time concurrency enables one to harness the computa.tiona.1 power available on large-sea.le multicomput­ ers. Timing results obtained on an Intel iPSC/2, an Intel iPSC/860 and the Intel Touchstone Delta. a.re presented.