Based on the contemporary shared memory Symmetric Multi Processing parallel machines (SMP), and the directive parallel programming platform, this paper discusses optimization and parallelization of a sparse linear equations solver package MFS for reservoir simulation software with more than one million nodes.

In the first part, the Riemann solvers in Godunov-type schemes are considered in the hyperbolic conservation laws systems.

So far,most syntactic parsers neglect the punctuations or oversimplify their functions.

We developed a high performance algebraic solver for nonlinear systems discretized from two-dimensional energy equations with three temperatures by a nine point scheme.