Certified reduced basis method in the Galerkin and Collocation frameworks

Yanlai Chen

(UMass Dartmouth)

The reduced basis method (RBM) is indispensable in scenarios where a large number of numerical solutions to a parametrized partial differential equation are desired in a fast/real-time fashion. These include simulation-based design, parameter optimization, optimal control, multi-model/scale simulation etc. Thanks to an offline-online procedure and the recognition that the parameter-induced solution manifolds can be well approximated by finite-dimensional spaces, RBM 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. In this talk, I will give a brief introduction of the RBM and discuss recent and ongoing efforts to develop RBM in the Galerkin and Collocation frameworks including applications to various electromagnetic problems.

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