I was (2006-2008) working on a project with Dr.Peterson where we are researching the speed up potential of a parallel implementation of Reduced Order Modeling for time-dependent/time-evolution applications involving the need for real-time computations of nonlinear partial differential equations.
We are combining the Reduced Order Modeling approach to solving nonlinear partial differential equations with the Parareal Algorithm as introduced by Lions in 2001. On March 31 2006 I presented some of my preliminary results at the SIAM-MAA regional conference at Auburn University as a contributed paper talk.
We wrote up some of our results for publication in Applied Math Letters. Here is a pre-print version for those interested, Combining the parareal algorithm and reduced order modeling for time dependent partial differential equations C.Harden and J.Peterson, submitted AML 2006
I presented this work a the SIAM conference on Computational Science and Engineering in Costa Mesa, California in February 2007.
I presented this poster at the SIAM conference on Parallel Processing for Scientific Computing in Atlanta, Georgia, PP08. Here is a copy of the poster for anyone interested. The Parareal Algorithm and Reduced Order Modeling
Here are a copy of my full set of slides that were to be used for my thesis defense presentation, prior to being slimmed down for the purpose of meeting the time constraints. Real Time Computing with the Parareal Algorithm - Thesis Defense Presentation
My new research direction for my dissertation work involves investigating the effects of thermal conductivity on Rayleigh-Taylor fluid instabilities in the context of inertial confinement fusion applications for the production of clean energy.
Here is a poster I'm presenting at this years Computational Exposition that is an overview of the work I'm doing.Expo Poster
Here is a full copy of my Ph.D prospectus with much more details on the research project.Ph.D Prospectus Slides