The traditional data distribution for partitioned grids places a partition on each processor plus shadow copies of the nearest neighboring grid elements of adjacent processors. This is insufficient for an efficient parallel multigrid method, resulting in either too much communication or loss of optimal order convergence depending on how the multigrid is parallelized.
A new approach to data distribution has been developed, called the full domain partition. 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 full domain partition, a parallel multigrid method can maintain a multigrid rate of convergence while sending only two messages per V-cycle. The full domain partition also accommodates parallel implementation of adaptive refinement and partitioning.
Mitchell, W.F., The Full Domain Partition Approach to Distributing Adaptive Grids, Applied Numerical Mathematics, 26 (1998) pp. 265-275, special issue for the proceedings of Grid Adaptation in Computational PDEs: Theory and Applications. (gzipped postscript, 102k)
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