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K-State Today

May 3, 2012



Brown University mathematics professor to present ninth Brent P. Smith Memorial Lecture today

By Reta McDermott

Jan Hesthaven, professor of applied mathematics at Brown University, will give the ninth Brent P. Smith Memorial Lecture at 2:30 p.m. today in 1018 Throckmorton Hall. His lecture is "Reduced Models You Can Believe In."

In this talk Hesthaven will present an overview of recent and ongoing efforts to develop reduced basis methods for which one can develop a rigorous a posteriori theory, hence certifying the accuracy of the reduced model for parametrized linear PDEs. This is in contrast to most previous attempts to develop reduced complexity methods that, while used widely and of undisputed value, are often heuristic in nature and the validity and accuracy of the output is often unknown. This limits the predictive value of such models. 

We outline the theoretical and computational developments of certified reduced basis methods, drawing from problems in electromagnetics and acoustics. The performance of the certified reduced basis model will be illustrated through a number of examples to highlight the major advantages of the proposed approach and discuss challenges associated with high-dimensional problems.