Research

Submitted by inducer on Sat, 05/04/2008 - 01:15

Current Projects

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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)

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DG on GPUs

Discontinuous Galerkin methods are rather arithmetically intense, and they access computational data in a mostly local and ordered fashion. It is therefore natural to ask whether DG would be a good fit for a the massively parallel computation capabilities of moden graphics processing units (GPUs). Working closely with Tim Warburton at Rice, I found that a practical, DG-based 3D Maxwell solver can outperform a current-generation CPU by factors between 40 and 60. We are presently extending our methods towards multi-GPU parallelism and more challenging equations.

Advisors: Jan Hesthaven (Brown), Tim Warburton (Rice)

  • AK, Tim Warburton, Jeff Bridge, Jan S Hesthaven, Nodal Discontinuous Galerkin Methods on Graphics Processors. Journal of Computational Physics, Volume 228, Issue 21, 20 November 2009, Pages 7863-7882. (arXiv, Brown SC Report, JCP)

Past Projects

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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