ZIB Colloquium: Reduced order models for simulation & control in fluid dynamics

Alfio Quarteroni, (in collaboration with A. Manzoni and F. Negri) CMCS - Modelling and Scientific Computing, MATHICSE - Mathematics Institute of Computational Science and Engineering, EPFL - Lausanne, Switzerland

Parametrized problems governed by PDEs occur in several applied contexts ranging from optimal control and/or design problems to inverse identification problems. Parameters may arise from physical coefficients, the geometrical configuration, or the control/design variables themselves. Solving these problems is rather challenging because of their large scale and iterative nature. Projection-based reduced-order models (ROMs) provide efficient strategies to tackle parametrized optimization and control problems, thanks to Offline/Online computational stratagems, a posteriori error estimates, and the use of low-dimensional approximation spaces. In this talk I will recall the mathematical concepts behind Reduced Order Models, present some new results, and address a few examples for the efficient simulation and optimization of flow problems arising in the haemodynamics context.

REFERENCES [1] T. Lassila, A. Manzoni, A. Quarteroni, G. Rozza. Model order reduction in fluid dynamics: challenges and perspectives. In Reduced Order Methods for Modeling and Computational Reduction, A. Quarteroni & G. Rozza (Eds.), Springer MS&A Series, Vol.9, pp. 235-274, 2014. [2] A. Manzoni. Reduced models for optimal control, shape optimization and inverse problems in haemodynamics. PhD thesis, N. 5402, E ́cole Polytechnique F ́ed ́erale de Lausanne, 2012. [3] F. Negri, G. Rozza, A. Manzoni, and A. Quarteroni. Reduced basis method for parametrized elliptic optimal control problems. SIAM J. Sci. Comput. 35 (5):A2316- A2340, 2013.