Thesis defence J.T. Zimmerling: wave equations
02 July 2018 12:30 - Location: Aula, TU Delft - By: webredactie
Model Reduction of Wave Equations: Theory and Applications in Forward and Imaging. Promotor 1: Dr. R.F. Remis (EWI); Promotor 2: Prof.dr. H.P. Urbach (TNW).
This thesis is about reduced-order modeling of the equations that describe the dynamics of wave propagation. In reduced-order modeling, the aim is to systematically develop a small model that describes a complex system without losing information that is valuable for a specific application. Evaluating such a model is computationally much more efficient than direct evaluation of the unreduced system and in the context of imaging it can lighten the computational burden associated with imaging algorithms. The central question is, of course: How does one construct a model that describes the wave dynamics relevant to a particular application?
In this thesis, we discuss different choices for the subspaces that are used for projection in model-order reduction. In particular, we show which types of subspaces are effective for wavefields that are localized and highly resonant and how to efficiently generate such subspaces by exploiting certain symmetry properties of the wave equations. We illustrate the effectiveness of the resulting reduced-order models by computing optical wavefield responses in three-dimensional metallic nano-resonators.
Not all wavefields are determined by a few resonances, of course. Waves can also travel over long distances without losing information; a property that is used by mobile phones every day. In this thesis, we present a so-called phase-preconditioning reduction method, in which a specific subspace is generated that explicitly takes the large travel times of the waves into account.
Finally, we show how reduced-order modeling techniques can be incorporated into advanced nonlinear imaging algorithms.
For access to theses by the PhD students you can have a look in TU Delft Repository, the digital storage of publications of TU Delft. Theses will be available within a few weeks after the actual thesis defence.