Scientific Computing Seminar Cecilia Pagliantini (TU/e)

Structure-preserving dynamical model order reduction of Hamiltonian systems

20 May 2022 from 11 a.m. to 20 May 2022 noon CEST (GMT+0200)
CWI, room L120

Cecilia Pagliantini (Eindhoven University of Technology): Structure-preserving dynamical model order reduction of Hamiltonian systems

In this talk we will consider reduced basis methods (RBM) for the model order reduction of parametric Hamiltonian dynamical systems describing nondissipative phenomena. The development of RBM for Hamiltonian systems is challenged by two main factors: (i) failing to preserve the geometric structure encoding the physical properties of the dynamics, such as invariants of motion or symmetries, might lead to instabilities and unphysical behaviors of the resulting approximate solutions; (ii) the local low-rank nature of transport-dominated and nondissipative phenomena demands large reduced spaces to achieve sufficiently accurate approximations. We will discuss how to address these aspects via a structure-preserving nonlinear reduced basis approach based on dynamical low-rank approximation. The gist of the proposed method is to evolve low-dimensional surrogate models on a phase space that adapts in time while being endowed with the geometric structure of the full model. If time permits, we will also discuss a rank-adaptive extension of the proposed method where the dimension of the reduced space can change during the time evolution.

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