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Ultra-efficient and Robust Reduced Basis Method with Applications to Uncertainty Quantification
Date: 2017/12/26             Browse: 43

Speaker:      Assistant Prof. Yanlai Chen. UMASSD

Time:          Dec   26.   14:00   —   15:00 

Location:    Room 1A-200, SIST Building

Host:          Prof. Qifeng Liao


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. 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 and accurate evaluation is critical.

After giving a brief introduction of the RBM, this talk will show our recent work on novel approaches for speeding up the offline portion of the approaches by around 6-fold, and new residual-based and residual-free strategies for circumventing error stagnation that is traditional of the classical RBM. If time permits, we will talk about the integration of RBM into the gPC framework for uncertainty quantification that is capable of significantly delaying the curse of dimensionality.


Yanlai Chen received his B.S. degree in Mathematics from University of Science and Technology of China (USTC), in 2002, M.S. in Computer Science and Engineering from Department of Computer Science and Engineering , and Ph.D. in Mathematics from School of Mathematics, University of Minnesota, in 2007. Prof. Cockburn, Bernardo was his thesis advisor. He then worked as a Postdoctoral Researcher supervised by Prof. Hesthaven Jan and Prof. Maday Yvon at Brown University. Dr. Chen joined Department of Mathematics, University of Massachusetts Dartmouth in August 2010, as an Assistant Professor in Mathematics. He was promoted to Associate Professor with tenure in 2016.

SIST-Seminar 17068