Present. Since January 2009 I've been an assistant professor at UNM.
Past. From August 2006 until December 2008, I was in the
Division of Applied Mathematics at Brown University, working for
Jan S.
Hesthaven and physics groups at Cornell and Caltech as part of
an NSF grant devoted to spectral methods for the Einstein equations.
Over a number of years members of the CaltechCornellCITA collaboration
(chiefly Lawrence E. Kidder, Harald P. Pfeiffer, and Mark A. Scheel)
have written a multidomain spectral code, SpEC
(spectral Einstein code).
The relativity groups at Caltech, Cornell, and CITA (Canadian Institute
of Theoretical Astrophysics) are using SpEC to generate and evolve initial
data describing the inspiral of binary blackholes. I've incorporated
various implicitexplicit (IMEX) ODE solvers into the TimeStepper
module of SpEC, and the project [with H. Pfeiffer (CITA) and
Geoffrey Lovelace (CSU, Fullerton)] aims to sidestep the Courant limit
in binary evolutions by using an IMEX timestepper such as additive
RungeKutta. This should be feasible since the solutions (well
before merger) are quasistationary in a corotating frame.
Over the 20052006 academic year I worked as a postdoc in
Mathematics & Statistics here at UNM
for Thomas M. Hagstrom
(now at SMU) on radiation boundary conditions and numerical wave
propagation, and I'm still working on boundary conditions for the wave
equation in the presence of sharp corners or edges. Over 20042005 I was
a research assistant professor of physics at
the CGWA in Brownsville
TX, working for
Richard H. Price
on the periodic standing wave (PSW)
approximation for binary inspiral. This ongoing work involves
application of spectral methods with integration preconditioning to
the mixedtype PDE cropping up in PSW problems.
Education. I did graduate work in applied mathematics at the
University of North
Carolina, studying numerical solutions to partial differential equations
under Michael L.
Minion. My dissertation, Rapid
Evaluation of Radiation Boundary Kernels for TimeDomain Wave
Propagation on Blackholes, numerically implemented
radiation outer boundary conditions for the ReggeWheeler equation, an
incarnation of the (singly) confluent Heun equation. This work was based
on an approach developed for the ordinary wave equation by Alpert,
Greengard, and Hagstrom [SIAM J. Numer. Anal. 37 (2000) 1138].
Far past. Earlier I wrote a physics dissertation in general relativity
(UNC, June 1994) under the direction of James W. York. My physics dissertation
reformulated the BrownYork twosurface integral definitions of gravitational
stress, energy, and momentum in terms of Ashtekar variables. The BrownYork
expressions stem from HamiltonJacobi theory as applied to the "Trace K" action,
the EinsteinHilbert action plus appropriate boundary terms. Ashtekar variables
are a YangMills chart (the Hamiltonian variables are A and E) on
the phase space of general relativity. As a relativist, I worked as a postdoc
at the InterUniversity Centre for Astronomy and Astrophysics (Pune, India)
from 1994 to 1995 and at the Technische Universitaet Wien (Vienna, Austria)
from 1995 to 1997. My interests in theoretical GR center around definitions of
gravitational energy, and I have collaborated with Alexander N. Petrov of Moscow State
University's Sternberg Astronomical Institute.
Teaching. Over the years, I've gotten
interested in teaching undergraduate math and physics, and have
experimented with several different instruction methods
(see my Teaching Statement). This Fall 2013 I am teaching
CSMath 471 (introduction to scientific computing)
and Math 576 (numerical linear algebra).
The 471 course webpage is on UNM Learn.
