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:
- the accurate modeling of physical systems involving
disparate time and space scales,
- the development and use of highly-accurate and efficient
time evolution algorithms for stiff multi-rate problems,
and
- the investigation of discretization and solution methods
that retain constraint-preserving properties of PDE systems.
I am pursuing these investigations in the context of 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:
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
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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