Research
Discontinuous Galerkin Methods and Electromagnetics
My advisor and I research multilevel (domain decomposition and multigrid) preconditioners for high-order discretizations of problems in electromagnetics. Stabilization terms enforced in the numerical fluxes of many Discontinuous Galerkin schemes greatly impact the (near) null-space of the resulting algebraic system. We investigate approaches to improve the conditioning of the problem. Project supported by NSF DMS 06-12448.
Strength Of Connection In Algebraic Multigrid
My other research track involves strength of connection in algebraic multigrid. On this project, I collaborate with Dr. Raymond Tuminaro, of Sandia National Labs and with my advisor. We are currently working on a paper outlining a new strength measure that is used in a version of Ray's smoothed aggregation code.
Publications
- Howle V., Schroder J., Tuminaro R., "The Effect of Boundary Conditions Within Pressure Convection Diffusion Preconditioners." Sandia National Labs Technical Report# 2006-446. July, 2006.
- Schroder J., Tuminaro R., Olson L., "Generalized Strength of Connection in Algebraic Multigrid." CSRI Summer Proceedings 2007. pp. 12-26. 2007.
Presentations
- Stability and Load Balancing in a NASA Global Circulation Model, Southeast ACM Conference, November 22, 2003.
- A General Strength-of-Connection Concept in AMG, Tenth Copper Mountain Conference on Iterative Methods, April 7, 2008.
Software Projects
- In conjunction with my research on higher-order Discontinuous Galerkin (DG) discretizations, I have written a 2-D DG code in MATLAB that discretizes the Helmholtz problem using one of six DG formulations. Polynomial orders from 1 to 11 are supported on simplex meshes stored in .neu format. Here is a summary paper on DG in 2-D that is meant to be a tutorial and a record of my learning process while deciphering the specifics of the implementation.
- In ML, I implemented an energy minimization algorithm for prolongator generation and an experimental strength of connection measure.
- I am a developer for PyAMG, an open source Python implementation of both classic algebraic multigrid (AMG) and smoothed aggregation style AMG.
Last updated June, 2007