New Math Models to Pick Up Where Computers Fail

With the great advances in computer in the recent years, many real-world processes are still so complex that defy the capability of even the most advanced supercomputers that’s why a call is being made to help.

As part of that effort, Us department of Energy has given a grant of $ 647,000 to Oregon State University to have advanced mathematics pick up where sheer computing power is inadequate.

The OSU mathematicians will be trying to model the flow of fluid through a porous medium, such as water through soil. It may sound simple, but in practice this can be so extraordinarily complex that there are still more questions than answers.

The program tackles problems of “multi-scale mathematics” – questions that span time scales from fractions of a second to years, and the atomic level to whole watersheds. The problems are so vast they cannot easily be broken down into simpler questions that could be solved using traditional mathematical techniques and models.

Even in the study of something as basic as water moving through soil, what you see depends on what window you look through, Showalter said.

Showalter said that conceptually, it’s similar to trying to describe the path of a butterfly on a long migration, rather than the up-and-down motion of its body with each cycle of its wings. Existing mathematics is able to do this averaging or “upscaling” in many cases.

Primary investigators on the OSU research will try to create new mathematical models that are able to tackle these topics, and then do analysis and simulation to study their accuracy.

With success, they said, someday the problems may be simplified enough that a supercomputer can handle them.






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