Research

Current Projects

High-Order Unstructured Particle-in-Cell

For many problems in Plasma physics, the Particle-in-Cell or “PIC” method is the only computationally feasible method of simulation. However, few existing PIC codes take advantage of the features of modern EM solvers, such as the benefits offered by high-order accurate approximations and unstructured meshes. My goal is to find out what it takes to develop an advanced PIC solver that leverages these (and other) recent advances. We hope that this solver will be able to extend the reach of PIC simulations to areas where very long time integration or very high accuracy is desired. If you’d like to get a visual idea of what I’m doing, you may view my research gallery.

Advisor: Jan Hesthaven, Brown

Past Projects

Computation of Maximally-Localized Wannier Functions

This is the project I pursued for my Diplom thesis at Universität Karlsruhe in Germany. The idea here is to compute specialized basis functions allowing the efficient computation of dispersion relations for large photonic crystals. My approach involved a second-order finite-element-based eigensolver and a CG-derived minimization procedure.

You may read my thesis (English, PDF). A gentler introduction is also available on the talks page.

Advisor: Willy Dörfler, Karlsruhe