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\bf {A brief summary of my research interest} \\
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My research interest is in the field of numerical relativity.  Since the
Einstein equations are a set of many coupled equations with changing 
length scales in time, this problems are extremely computationally intensive.
To handle these problems, we must 
learn to use the latest numerical algorithms, as we will have to use the next 
generation of computers, capable of  Tera-flop speeds and Giga-byte storage.
A major goal of numerical relativity is to be able
to predict characteristics of the gravitational radiation of astrophysical
events, which should be observed with the LIGO/VIRGO gravitational
detectors.
Computationally,
these problems all deal with solving highly Nonlinear Partial Differential
 Equations. This is where my research interest lies.   


Over the past three years, I have worked with the initial value problem 
for two black holes, along with Matthew Choptuik and Richard Matzner.  
I have written numerous solvers 
for elliptic partial differential equations, with 
non-trivial boundary conditions.  Some of the more popular techniques that
were employed include:  
Successive Over Relaxation methods, Domain
Decomposition, and Multigrid techniques. 
I have also developed several
adaptive codes based on the Berger and Oliger, Choptuik algorithm.  Adaptive
codes are powerful since they allow the computational work to be proportional
to the physics being modeled. 
The significance of this work is
that it allowed us to develop a set of tools which can be used in 
evolution codes.  One such tool, deferred correction, helped us achieve
high order accuracy using Cartesian coordinates for 'spherical' holes, using
low order relaxation. 
One of my goals is to parallelize these algorithms, to aid 
in the development of a three dimensional, two black hole, evolution code.
Since my codes can handle general boundary conditions for elliptic partial
differential equations, it should be trivial to model other physical processes.
This complies with the philosophy
of computer coding here at Texas, which is to design the codes 
that will be reusable for all different types of problems with a minimal
amount of rewriting.

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