Parallel computers hold much promise for scientific computation. So a great deal of effort has been devoted to finding ways to parallelize linear equation solvers.

However in fully implicit reservoir simulators the real problem is the solution of non-linear equations. This paper shows how a judicious combination of linear and non-linear solution techniques can lead to the fastest overall simulator. It uses a combination of an approximate iterative solution of the Jacobian and a Quasi-Newton method.

The proposed method makes it possible to use the highly parallelizable Jacobi matrix solution techniques, which are poorly convergent, and still get good serial performance.

Experiments on a parallel computer show that even with a highly parallel method, problem sizes need to be quite large to get good efficiency.

The proposed method can also be used to speed up serial programs by simply using a good serial technique to iteratively solve the linear equations.

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