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
No registration fee. Please register online. Apply Online
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.
|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|