Ultra-efficient and Robust Reduced Basis Method with Applications to Uncertainty Quantification
Yanlai Chen, Brown University
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.
After giving a brief introduction of the RBM/RCM, this talk will show our recent work on novel approaches for speeding up the offline portion of the RBM/RCM 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, significantly delaying the curse of dimensionality.