Date & Time:
Monday, December 12, 2016; 12:00 PM
Models of reduced computational complexity is indispensable in scenarios where a large number of numerical solutions to a parametrized problem are desired in a fast/real-time fashion. These include simulation-based design, parameter optimization, optimal control, multi-model/scale analysis, uncertainty quantification. Thanks to an offline-online procedure and the recognition that the parameter-induced solution manifolds can be well approximated by finite-dimensional spaces, reduced basis method (RBM) and reduced collocation method (RCM) can improve efficiency by several orders of magnitudes. The accuracy of the RBM solution is maintained through a rigorous a posteriori error estimator whose efficient development is critical and involves fast eigensolves.
In this talk, I will give a brief introduction of the RBM/RCM, and explain how they can be used for data compression, face recognition, and significantly delaying the curse of dimensionality for uncertainty quantification.
Department of Mathematics at the University of Massachusetts Dartmouth
Yanlai Chen is an Associate Professor in the Department of Mathematics at the University of Massachusetts Dartmouth where he started in August 2010. He spent the previous three years at Brown university as a postdoctoral research associate. Dr. Chen's degrees include a B.S (Mathematics) from University of Science and Technology of China (USTC) obtained in 2002, a M.S. (Computer Science) and a Ph.D. (Mathematics) from University of Minnesota Twin Cities obtained in 2007.
His research interests are in numerical analysis and scientific computing, in particular, adaptive discontinuous Galerkin finite element method, hybridizable discontinuous Galerkin method, reduced basis method, and uncertainty quantification. These methods concern topics such as the design and analysis of methodologies that can allocate computational resources to where it is needed, how to solve certain equations more efficiently without losing accuracy, how to couple available methods utilizing their respective advantages, and how to improve efficiency for repeated simulation of problems with varying parameter.