Model Reduction on Manifolds

Organization:

Funded by:	Sectorplan Beta en Techniek
PhD:	H.L. Mu MSc (Hongliang) PhD Candidate +31534893418  h.l.mu@utwente.nl Building: Zilverling 3022 Personal page
Supervisors:	Chair HS: prof.dr. H.J. Zwart (Hans) Professor in Physical Systems and Control/Chair Mathematics of Systems Theory +31534893464  h.j.zwart@utwente.nl Building: Zilverling 3042 Personal page Daily Supervisor: dr. S.M. Glas (Silke) Assistant Professor +31534899687  s.m.glas@utwente.nl Building: Zilverling 3046 Personal page
Collaboration:

Description:

Many physical phenomena, for example a pendulum, can be represented by dynamical systems via mathematical modelling. For these systems, model reduction (MOR) is a widely used method to reduce the computational complexity. It has been shown that linear-subspace MOR (also called classical MOR) can work well if a fast decay of the Kolmogorov n-widths is observed. For advection-dominated or wave-like problems, however, the decay of the Kolmogorov n-widths is expected to be slow. For these classes of problems, classical MOR would need a large amount of basis functions to provide an accurate reduced order model (ROM), resulting in an expensive computation. Thus, we explore different nonlinear approximation methods, e.g., MOR on manifolds. 

 In this project, we will develop MOR on manifolds - both theoretically and applied - to increase the accuracy in the ROMs compared to classical MOR. At the same time, we will assure that the physical structure of the original system is retained in the reduced model

Pictures: