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Abstract : |
The conjugate gradient method is a powerful algorithm for solving well-structured sparse linear systems that arise from partial differential equations. The broad application range makes it an interesting object for investigating novel architectures and programming systems. In this paper we analyze the computational structure of three different conjugate gradient schemes for solving elliptic partial differential equations. We describe its parallel implementation on the Cedar hierarchical memory multiprocessor from both angles, explicit manual parallelization and automatic compilation. We report performance measurements taken on Cedar, which allow us a number of conclusions on the Cedar architecture, the programming methodology for hierarchical computer structures, and the contrast of manual vs automatic parallelization. 1, |
