Workshop Twente 2020 Online meeting

NDNS+ WORKSHOP June 22-23, 2020      online meeting

22-23 June 2020 

Speaker: dr. Cecilia Pagliantini - Eindhoven University of Technology

Cecilia Pagliantini: GAMM Junior – Department of Mathematics | ETH ...

Title: Structure preserving reduced order models for parameterized Hamiltonian systems

Parameterized differential equations are ubiquitous in applied science and are characterized by input parameters that describe possible variations in geometric configuration or physical properties of the modeled system. When real-time and many-query resolutions of such problems are required, computational methods need to face prohibitively high computational costs to provide sufficiently accurate and stable numerical solutions. To overcome this issue, model order reduction techniques construct low-complexity high-fidelity surrogate models that allow rapid and accurate solutions under parameter variation. However, many challenges remain to secure the robustness and efficiency needed for the numerical approximation of nonlinear time-dependent problems. After a brief introduction to reduce order models, we will discuss reduced basis methods for parameterized Hamiltonian dynamical systems describing nondissipative phenomena. In this case, standard formulations of reduced models do not guarantee the preservation of the geometric structure underlying the physical properties of the dynamics, like symmetries, invariants and conservation laws, and might lead to spurious results. We present structure preserving reduced basis methods that can effectively preserve the geometric structure during the reduction, by deriving surrogate models where the reduced phase-space inherits the geometric structure of the original dynamics.