Adaptive methods and rectangular partitioning problem

Partitioning problems for rectangular domains having nonuniform workload for mesh-connected SIMD architectures are discussed. The considered rectangular workloads result from application of adaptive methods to the solution of hyperbolic differential equations on SIMD machines. A new form of the partitioning problem is defined in which sub-meshes of processors are assigned to tasks, each task being a discretized rectangular sub-domain. The work per processor (i.e. the work density) is balanced among the K sub-rectangular meshes of processors. First, a formalization of the 1D problem is given and a O(Kn³) time and (Kn²) space optimal algorithm is proposed. A more efficient heuristic algorithm is also given for the 1D problem. Finally 2D heuristics are developed by projecting the weights on to a 1D array