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Computational Science Seminar by Anastasiya Protasov
Friday, October 22, 2021 1pm to 2pm
Virtual Event
Event Details
Anastasyia Protasov
Rice University
Balanced Truncation Based on Generalized Multiscale Finite Element Method for the Parameter-Dependent Elliptic Problem
We combine the generalized multiscale finite element method (GMsFEM) with the balanced truncation (BT) method to address a parameter-dependent elliptic problem. Basically, in progress of a model reduction we try to obtain accurate solutions with less computational resources. It is realized via a spectral decomposition from the dominant eigenvalues, that is used for an enrichment of multiscale basis functions in the GMsFEM. The multiscale bases computations are localized to specified coarse neighborhoods, and follow an offline-online process in which eigenvalue problems are used to capture the underlying system behaviors. In the BT on reduced scales, we present a local-global strategy where it requires the observability and controllability of solutions to a set of Lyapunov equations. As the Lyapunov equations need expensive computations, the efficiency of our combined approach is shown to be readily flexible with respect to the online space and a reduced dimension. Numerical experiments are provided to validate the robustness of our approach for the parameter-dependent elliptic model.
Location
Virtual Event
Department
- Natural Sciences & Mathematics
Contact Information
- John Zweck
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