Prof. Tommaso Taddei - Università di Bordeaux Sud Ovest The reduced basis method is a model reduction techriique to reduce the marginal(i.e., in the limit of many queries) cast of the solution to parametric systems. The course aims to provide an introduction to the reduced basis method, with emphasis on computational mechanics applications.

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the course consists in 12 1.Sh sessions (11 lectures and 3 practical sessions). To allow students to focus on the main aspects of the RB methodology, a· Matlab implementation of the finite element meth̉d far 2D elliptic PDEs will be provided. 1. Lecture 1: introduction of the course and review of basic results of linear functional analysis. 2. Recitation 1: review of the finite element method; familiarization with a Matlab implementation of continuous Galerkin finite element method. 3. Lecture 2: data compression based on proper orthogonal decomposition; brief remarks on randomized methods. 4. Lecture 3: Galerkin reduced-order models; a posteriori errar estimation far linear problems. 5. Lecture 4: weak-Greedy algorithm. 6. Recitation 2:·. sampling. implementation of the weak Greedy algorithm; comparison with POD 7. Lecture 5: hyper-reduction based on reduced quadrature rules. 8. Recitation 3: implementation of the hyper-reduction t echnique . 9. Lecture 6: empiricaI interpolation method; S-Greedy variant. 10. Recitation 10 (1.Sh) : implementation of the EIM and SGreedy. 11. Lecture 7: geometrica! parameteri zat ions. 12. Lecture 8: advanced topics .(nonlinear approximations; component-based model arder reduction).

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P.D.1-1 - Gennaio