This paper describes parallel linear solvers of LSOR and preconditioned ORTHOMIN ( K ) on parallel computer based on T8OO Transputers and SUN workstation cluster ( with Ethernet network).

Both Algorithms show a high degree of parallel efficiency on Transputers, whereas only full impliicit method and large petroleum reservoir problems can observe a high efficiency on SUN workstation cluster.

The key issure in parallelization of reservoir simulator on workstation cluster is the improvement of communication speed.

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