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Fall 2002

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Mathematics and the Energy Crisis: Article by Beatrice Riviere     Page 4.
High Performance Computing
The gridding techniques, discretization methods, model development, and visualization are only as good as the computing power available. The demands of reservoir engineers to increase the complexity of their models has always grown with the availability of computing power. Innovations in parallel techniques have allowed engineers to go from only tens of reservoir cells in the 1960's to tens of millions of cells today. These techniques cover domain decomposition, efficient message-passing strategies, and enhanced linear equation solver formulations.

Pittsburgh Super Computer `LeMieux'
Excellent parallel performance is obtained not only on conventional, sophisticated parallel UNIX machines (such as the Pittsburgh Super Computer facilities), but also on clusters of PC's. Obtaining a cluster of PC's can be relatively inexpensive, and the Math Department is building such a system called SCREMS. However due to the problem of the explosion of information for reservoir simulators, there will continually be a need for further improvements in high performance computing.

There are other issues which should be continually addressed. Parallel linear equation solvers should be improved, especially for fully-implicit formulations; tubing hydraulics, surface facilities and pipeline networks should be better incorporated into the overall parallelization process; and static and dynamic load balancing should be optimized to take full advantage of any parallel simulation.

Conclusions
Research in many areas of applied mathematics can help with the current energy crisis. The problems in the oil industry are all interconnected: the grids are only as good as the discretization methods; the choice of discretization method may depend on the computing power available; and accurate predictions of future behavior rely on good optimization techniques as well as good gridding, discretizations, and models. Applied mathematics can really help extract energy in an environmental and efficient manner and can contribute to the design of the next generation of reservoir simulators.

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