Short Course on Reduced Basis Methods

Course Title

Reduced Basis Methods: Theory, Implementation and Applications


Yanlai Chen, Department of Mathematics, University of Massachusetts Dartmouth


Room 602, Pao Yue-Kong library, Shanghai Jiao Tong University

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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 development is critical and involves fast eigensolves. This short course will present an introduction of the RBM/RCM, their theoretical underpinning, all ingredients of the algorithm in its classical form, and some of our recent work on novel approaches for speeding up the offline portion of the RBM/RCM, and new residual-based and residual-free strategies for circumventing error stagnation that is traditional of the classical RBM. A Matlab-based software system will be demonstrated in the course. We will also talk about a data compression algorithm inspired by RBM, and the integration of RBM into the generalized Polynomial Chaos (gPC) framework for uncertainty quantification, significantly delaying the curse of dimensionality.


Date Time Lecture
December 13, 2017 9:00-11:40 Lecture 1
December 14, 2017 9:00-11:40 Lecture 2
December 15, 2017 9:00-11:40 Lecture 3

Tentative outline