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SCALLOP is a highly scalable solver and library for elliptic partial differential equations on regular block-structured domains. SCALLOP avoids high communication overheads algorithmically by taking advantage of the locality properties inherent to solutions to elliptic PDEs. Communication costs are small, on the order of a few percent of the total running time on up to 1024 processors of NPACI's and NERSC's IBM Power-3 SP sytems. SCALLOP trades off numerical overheads against communication. These numerical overheads are independent of the number of processors for a wide range of problem sizes. SCALLOP is implicitly designed for infinite domain (free space) boundary conditions, but the algorithm can be reformulated to accommodate other boundary conditions. The SCALLOP library is built on top of the KeLP programming system and runs on a variety of platforms.