The Full Domain Partition Approach to DistributingAdaptive

Adaptive reenement has been shown to be an eeective means of speeding up the solution of partial diierential equations. Adaptive multilevel methods combine multigrid iteration with adaptive reenement to produce fast O(N) solutions on sequential computers. However, many problems of interest require parallel computers. While adaptive reenement, multigrid and parallel computers are individually achieving wide spread use in applications, the combination of all three is still a research topic. In this paper we describe the full domain partition (FuDoP) distribution of adaptively reened grids over a distributed memory parallel computer. In the Fu-DoP approach, each processor has a compatible grid that covers the full domain, but with reenement connned to the processor's partition of the total grid. Outside the partition area, reenement is limited to that required for compatibility and leads to a small number of extra grid elements. With the FuDoP distribution, a parallel multigrid method can maintain a multigrid rate of convergence while sending only two messages per V-cycle. FuDoP also accommodates parallel implementation of adaptive reenement and partitioning.