A Parallel Solution of Large-Scale Heat Equation Based on Distributed Memory Hierarchy System

A parallel scheme for distributed memory hierarchy system is presented to solve the large-scale three-dimensional heat equation. Since managing interprocess communications and coordination is the main difficulty with the system, the local physics/global algebraic object paradigm is introduced. Domain decomposition method is used to partition the modeling area, as well as the intensive computational effort and large memory requirement. Efficient storage and assembly of sparse matrix and parallel iterative solution of linear system are considered and developed. The efficiency and scalability of the parallel program are demonstrated by completing two experiments on Linux cluster, in which different preconditioning methods are tested and analyzed. And the results demonstrate this method could achieve desirable parallel performance.

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