Parallel Random Surfaces
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Load Balancing - Poor load balancing on SIMD machines, since the number of links per node can range from 3 to 20.
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Dynamic Domain Decomposition - Dynamic mesh means that neighboring points will change during the simulation and eventually be on distant processors, requiring substantial non-local communication. Need dynamic load balancing to preserve local communications (c.f. dynamic adjustment of arrays to keep neighboring points in fast cache memory on sequential machines.
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Detailed Balance - The most difficult problem is to preserve detailed balance. A site cannot be updated at the same time as the other sites on which its value depends. For a regular 2-d grid, use black/red checkerboard update, For a dynamic, irregular grid, identifying independent sites is a time-consuming problem which must be redone before every iteration.
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Irregular Adaptive Grids for PDEs - This problem has much in common with parallel algorithms for solving PDEs on irregular, adaptive grids (e.g. CFD)
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Implementation - Currently developing parallel code for CM-5 and Intel Delta
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