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Jay Gopalakrishnan: Simulate right - Use mathematics
Jay Gopalakrishnan: Simulate right - Use mathematics

The success of scientific computation in recent decades in the design and prediction of complex engineering and biological systems has elevated it into a scientific methodology distinct from the traditional theoretical and experimental methodologies. Dr. Gopalakrishnan argues that the key to this success has been numerical algorithms founded on sound mathematical principles. This opinion shapes his research attitudes.

He occupies himself with the inner workings of the tools for scientific computation. He loves to teach the math behind these tools. In classroom, he shows how a wrong choice of method can lead to simulations with incorrect conclusions.  In his research, he designs and analyzes new numerical methods for solving partial differential
equations, which are at the heart of various physical models. He co-invented two relatively recent classes of numerical methods, now known in the discipline as HDG (hybridized discontinuous Galerkin methods) and DPG (discontinuous Petrov Galerkin) methods.

When faced with a problem needing a simulation, he prefers to get a solution approach with a mathematical guarantee, even if it takes more time, rather than get some makeshift heuristics going quick. He emphasizes the role of mathematics in his research: Math tells us how to develop methods with accuracy guarantees.  Math tells us how to make solution techniques faster.

His research into the mathematical foundations of new and old numerical methods is funded by NSF (National Science Foundation).  His group is currently engaged in developing novel simulation techniques for acoustic and electromagnetic wave propagation, an effort sponsored by AFOSR (Air Force Office of Scientific Research).

While not wedded to any particular application area, the needs of specific applications often drive Dr. Gopalakrishnan's research. For example, through a DARPA (Defense Advanced Research Projects Agency) subcontract, he helps a team of engineers trying to understand lightning initiation and propagation near Kennedy Space Center. He provides techniques to simulate changes in electrical fields that accompany or trigger lightning. Previously, he worked with engineers in Medtronic Inc., to design a full-featured simulation of their cardiac ablation electrodes.

Dr. Gopalakrishnan left his full professorship at University of Florida to take up the Maseeh Distinguished Chair at Portland State University. Ever since his arrival about two years ago, he has been focused on building a visible and scholarly group in computational mathematics within PSU. He serves on the editorial board of four journals and is a popular speaker at conferences.  The photo shows him speaking at Brown University’s ICERM (Institute for Computational and Experimental Research in Mathematics), the newest of the NSF's Mathematical Sciences Research Institutes.”