This paper presents a new technique for solving the linear equations arising in reservoir simulation using multiple processors in parallel. The parallel algorithms for the Nested Factorization method are developed and implemented on a network cluster of highperformance IBM RISC System/6000 workstations as well as on a network of transputers. It is demonstrated on different 3-D data sets varying from 10,000 to 750,000 grid cells that a very high efficiency is achieved on MIMD, local memory, parallel platforms.

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