The full domain partition approach to distributing adaptive grids

Adaptive refinement has been shown to be an effective means of speeding up the solution of partial differential equations. Adaptive multilevel methods combine multigrid iteration with adaptive refinement to produce fast O(N) solutions on sequential computers, where N is the number of grid elements. However, many problems of interest require parallel computers. While adaptive refinement, multigrid and parallel computers are individually achieving widespread 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 refined grids over a distributed memory parallel computer. In the FuDoP approach, each processor has a compatible grid that covers the full domain, but with refinement confined to the processor's partition of the total grid. Outside the partition area, refinement 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 with only two communication steps per V-cycle. FuDoP also accommodates parallel implementation of adaptive refinement and partitioning. (C) 1998 Elsevier Science B.V.