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Brief introductory slides on my research (Fall 2008)

General Research Interests

My primary field of research is applied mathematics, specifically the sub-disciplines of scientific computation and numerical analysis. In the fast-developing field of scientific computation, there are three broad research thrusts that together aim to allow mathematical insight and innovation to make a difference in the physical, biological and engineering sciences: the incorporation of increased realism into mathematical modeling systems; the development of increasingly robust and accurate numerical methods for solution of mathematical models; and the development of computational algorithms to allow for efficient solution of these problems on increasingly-larger computational hardware.

In my own research, I have contributed to each of the aforementioned challenges through investigations on the algorithmic development and computational solution of coupled multi-physics systems of partial differential equations. These applications arise in real-world applications ranging from fusion energy to cosmological astrophysics and materials science. In these areas, I strive to explore three fundamental applied mathematics issues:

  1. the accurate modeling of physical systems involving disparate time and space scales,
  2. the development and use of highly-accurate and efficient time evolution algorithms for stiff multi-rate problems, and
  3. the investigation of discretization and solution methods that retain constraint-preserving properties of PDE systems.
I pursue these investigations both through the general development of numerical methods for solving general multi-rate systems, as well as through a number of highly collaborative physics applications: the modeling of solid-state phase transformations and thermodynamics in shape memory alloys, simulations of macroscopic stability and refueling of fusion plasmas, calculations determining the physical processes underlying core-collapse supernova phenomena, and investigations of reionization physics within the early universe.

Pages Describing Specific Research Projects:

ARKode  [Solver library for evolution of multi-rate problems]

Shape Memory Alloy Modeling  [Multi-scale mathematical modeling and simulation]

Fusion Energy & Core-collapse Supernovae  [Algorithmic design and software for robust and efficient multi-physics problems]

Cosmic Reionization of the Early Universe  [Multi-scale, multi-physics modeling and petascale scientific computing]

Funding Support

    LLNL Subcontract (PI), 2011-2016.

    DOE FASTMath SciDAC Grant (co-I; with L. Diachin et al.), 2011-2016.

    NSF AST Grant 1109008 (co-PI; with M. Norman), 2011-2014.

    DoD/ARO DURIP Grant (co-PI; with T. Hagstrom, S. Xu and Y. Zhou), 2011-2014.

    DOE INCITE Awards "How High Redshift Galaxies Reionized the Universe" (co-PI; with M. Norman & R. Harkness), 2011-2012, 2012-2013.

    LBL Subcontract 6925354 (PI), 2010-2011.

    NSF AAG Grant 0808184 (co-PI; with M. Norman), 2008-2011.

    NSF OCI Grant 0832662 (supporting; with B. O'Shea), 2009-2011.

    DOE SciDAC Grant ER25785 (co-PI; with D.E. Keyes et al.), 2006-2011.

    LLNL Subcontract B555750 (co-PI; with M. Holst), 2005.


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