The Importance of PDEs for Modeling and Simulation on Peta and Exascale Systems

As scientists and engineers tackle more complex problems involving multiphysics and multiscales and then seek to solve these problems through computation, the partial differential equation formulations which incorporate and more closely approximate the complex physical or biological phenomena being modeled will also be important to unlocking the approach taken on Peta and Exascale systems. Scientists and engineers working on problems in such areas as aerospace, biology, climate modeling, energy and other areas demand ever increasing compute power for their problems. For Petascale and Exascale systems to be useful massive parallelism at the chip level is not sufficient. I will describe some of the challenges that will need to be considered in designing Petascale and eventually Exascale systems. Through the combination of High Performance Computing (HPC) hardware coupled with novel mathematical and algorithmic approaches emerging from the original PDE formulations some efforts toward breakthroughs in science and engineering are described. While progress is being made, there remain many challenges for the mathematical and computational science community to apply ultra-scale, multi-core systems to “Big” science problems with impact on society. In conclusion, some discussion not only on the most obvious way to use ultra-scale, multi-core HPC systems will be given but also some thoughts on incorporating more physics in the algorithms derived from the PDE models which might allow us to better use such systems to tackle previously intractable problems.

Kirk E. Jordan, IBM T.J. Watson Research Center

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