Scientific Computing Seminar Cecilia Pagliantini (TU/e) — CWI Amsterdam
Cecilia Pagliantini (Eindhoven University of Technology): reduction of the order of dynamical models preserving the structure of Hamiltonian systems
In this talk, we will examine reduced basis methods (RBM) for the reduction of the order of the model of parametric Hamiltonian dynamical systems describing non-dissipative phenomena. The development of RBM for Hamiltonian systems is challenged by two main factors: (i) failure to preserve the geometric structure encoding the physical properties of the dynamics, such as motion invariants or symmetries, can lead to instabilities and non-physical behaviors of the resulting approximation. solutions; (ii) the low-rank local nature of transport-dominated and non-dissipative phenomena requires large reduced spaces to obtain sufficiently accurate approximations. We will discuss how to approach these aspects via a structure-preserving nonlinear reduced basis approach based on a lower-rank dynamical approximation. The essence of the proposed method is to evolve low-dimensional surrogate models on a time-adaptive phase space while being endowed with the geometric structure of the complete model. Time permitting, we will also discuss a rank-adaptive extension of the proposed method where the dimension of the reduced space can change over time.
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