General Research Interests
My primary field of research is applied mathematics,
specifically the subdisciplines of scientific computation and
numerical analysis. In the fastdeveloping 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 increasinglylarger
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
multiphysics systems of partial differential equations. These
applications arise in realworld applications ranging from
fusion energy to cosmological astrophysics and materials
science. In these areas, I strive to explore three fundamental
applied mathematics issues:
 the accurate modeling of physical systems involving
disparate time and space scales,
 the development and use of highlyaccurate and efficient
time evolution algorithms for stiff multirate problems,
and
 the investigation of discretization and solution methods
that retain constraintpreserving properties of PDE systems.
I pursue these investigations both through the general
development of numerical methods for solving general multirate
systems, as well as through a number of highly collaborative
physics applications: the modeling of solidstate phase
transformations and thermodynamics in shape memory alloys,
simulations of macroscopic stability and refueling of fusion
plasmas, calculations determining the physical processes
underlying corecollapse supernova phenomena, and investigations
of reionization physics within the early universe.
Pages Describing Specific Research Projects:
ARKode
[Solver library for evolution of multirate problems]
Shape Memory Alloy Modeling
[Multiscale mathematical modeling and simulation]
Fusion Energy & Corecollapse
Supernovae [Algorithmic design and software for robust and
efficient multiphysics problems]
Cosmic Reionization of the Early
Universe [Multiscale, multiphysics modeling and
petascale scientific computing]
Funding Support
LLNL Subcontract (PI), 20112016.
DOE FASTMath SciDAC Grant (coI; with
L. Diachin et al.), 20112016.
NSF AST Grant 1109008 (coPI; with M. Norman),
20112014.
DoD/ARO DURIP Grant (coPI; with T. Hagstrom, S. Xu and Y. Zhou),
20112014.
DOE INCITE Awards "How High Redshift Galaxies
Reionized the Universe" (coPI; with M. Norman & R. Harkness),
20112012, 20122013.
LBL Subcontract 6925354 (PI), 20102011.
NSF AAG Grant 0808184 (coPI; with M. Norman),
20082011.
NSF OCI Grant 0832662 (supporting; with B. O'Shea),
20092011.
DOE SciDAC Grant ER25785 (coPI; with
D.E. Keyes et al.), 20062011.
LLNL Subcontract B555750 (coPI; with
M. Holst), 2005.
