Professor Yanlai Chen , Dept of Mathematics, University of Massachusetts, Dartmouth |

Title:Ultra-efficient Reduced Basis Method and Its Integration with Uncertainty Quantification |

Abstract: 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 eigensolvers. After giving a brief introduction of the RBM/RCM, this talk will show our recent work on significantly delaying the curse of dimensionality for uncertainty quantification, and new fast algorithms for speeding up the offline portion of the RBM/RCM by around 6-fold. |