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Invitation to the Mathematical Colloquium
Wednesday, January 08, 2025, conference room (R107), 5 p.m. s.t.
Prof. Dr. Thomas Wick, Institute for Applied Mathematics at Leibniz Universität Hannover will speak on the topic: "Model Order Reduction Dual-Weighted Residuals: space-time goal-oriented error control for incremental POD-based ROM for time-averaged goal functionals"
Abstract: In this presentation, we utilize space-time formulations and space-time Galerkin finite element discretizations to treat single PDEs and linear-coupled PDEs. The objective is to prepare for incremental orthogonal proper decomposition as model order reduction technique in order to reduce the computational cost. In incremental orthogonal proper decomposition, new full order model snapshots are only added to the reduced model if some error tolerance exceeds a treshold. The error evaluation is based on goal-oriented concepts in which the goal functional represents some physics-inspired quantity of interest. This is realized as an optimal control problem in which the PDE serves as a constraint by minimizing the goal functional error between the full order model and the reduced order model. To this end, a backwards-in-time adjoint problem
must be computed. The algorithmic advancements are demonstrated for model problems such as the heat equation as well as benchmarks in porous media such as a three-dimensional footing problem.
There will be an opportunity for all interested parties to talk over coffee and tea in the conference room (R206) from 16:30.
Olaf Ippisch
Organizer: Institute of Mathematics, Erzstraße 1, 38678 Clausthal-Zellerfeld