Having 10 terabytes of computing in your laptop is very unlikely, but with cloud computing, the idea is not too far off. Dr. Mahadevan Ganesh presented his work, done in coordination with Dr. Jan Hesthaven of Brown University and Dr. Benjamin Stamm, at the first Math and Computer Science Colloquium of the Spring semester.
Titled “A Model Reduction Algorithm for Computational Electromagnetics,” Ganesh discussed methods to calculate problems that can take a large computer a significant amount of time to solve.
Ganesh began by introducing the idea that cloud computing at the consumer level could be the main source of computing power in 10 years. “But can it be done in scientific computing? Maybe in 25-30 years.”
He explained that the use of cloud computing will help decrease time to calculate systems of computations. The basic idea is that computations can be done “really fast at other’s expense.”
The proposed process is heavy with offline computations along with online simulations. In essence, the offline will be more of the mathematical calculations while the online will be the experimentation.
In Ganesh’s experiment, Ganesh plans to reduce some costly, yet necessary, calculations by the reduction of size of some of the systems used. As some of the systems grew to be tens of thousands by tens of thousands of elements, this would require a large amount of time for a computer to compute.
Ganesh continued to explained his simulation where a scenario of bodies were made and then particles would be sent into the scenario and exit with interaction information. Ganesh plans to input light and then have the output as radar cross section, or the intensity of the light afterwards.
Thus far, simulations have been done with a set of very few parameters. Ganesh wished to expand to the parameters “so that a model will work for any number of parameters even if you are working with 25 dimensions.”
But, every addition of a new parameter increases the offline workload. Ganesh explains that the end goal is to test a “reduced basis method” in which the heavy offline computations can be reduced and made more simple.
After some computations, Ganesh verified his calculations with the Maxwell-Equations as electromagnetic fields would be created from the interactions. This continued to explain the reduction process.
Ganesh explained that his experiment was done with a process from the Massachusetts Institute of Technology called Empirical Interpolation Method, which is a way to approximate parameters to a given required accuracy.
After a little bit more computation, Ganesh showed the results in which he found “the reduced basis method fits the actual results well and required much fewer calculations.”
Ganesh concluded that problems with many parameters can be solved with analysis and reduced models.