THE COMBINATION TECHNIQUE FOR THE SPARSE GRID SOLUTION OF PDE'S ON MULTIPROCESSOR MACHINES

Abstract

We present a new method for the solution of partial differential equations. In contrast to the usual approach which needs in the 2-D case [Formula: see text] grid points, our combination technique works with only [Formula: see text] grid points, where hn denotes the employed grid size. The accuracy of the obtained solution deteriorates only slightly from [Formula: see text] to [Formula: see text] for a sufficiently smooth solution. Additionally, the new method is perfectly suited for parallelization. On a machine with [Formula: see text] processors we get in practice an overall parallel complexity of only [Formula: see text]. The method can be generalized to higher dimensions. Then, the gain is expected to be even more dramatic. For the two-dimensional case, we report the results of numerical experiments obtained on a Transputer system and on the CRAY Y-MP.