After graduating in Mechanical Engineering, I went to graduate school
at the Federal University of Rio de Janeiro, Brazil, where I got a M.Sc.
degree in Applied Mathematics, writing my thesis on streamline methods
for flow in porous medium. Concurrently, I was working as a research
assistant in the Research and Development Center of Petrobras (the
Brazilian oil company), in the development of a streamline-based
reservoir simulator.
Now, when I am about to begin the third year of the Ph.D. program in
Mathematics at the Courant Institute of Mathematical Sciences, New York
University, my main interests are still the efficient numerical solution
of partial differential equations with applications to engineering
problems. Having fulfilled all other program requirements, I'll spend
the next couple of years fully devoted to my thesis research on Domain
Decomposition Methods (DDM), under the supervision of my advisor Prof.\
Olof B. Widlund. DDM are iterative methods for solving the often huge
systems of equations that arise from the discretization of partial
differential equations by the finite element method and, by their very
nature, are very suitable for implementation on distributed memory
parallel machines. The design, analysis, efficient implementation and
application of these methods are all interesting and challenging
projects, in which I would like to engage.
DDM can contribute one building block to an actual application code,
namely an efficient preconditioner for the linear system; this is
usually the computational kernel of the code. As such, it is natural to
have them implemented as modules of numerical libraries. In this line of
work, I am currently at the Argonne National Laboratory, working on a
summer project under the supervision of Dr.\ Barry Smith, one of the
developers of PETSc, one of the tools in ACTS toolkit. I have been
appointed a Wallace Givens Research Associate at the ANL for 12 weeks
and I am currently working in the implementation of Balancing
Neumann-Neumann and FETI methods as preconditioners in PETSc.
Since I am and will be working on specific numerical methods for
high-performance computing, as well as their applications to practical
problems, I believe it would be extremely valuable for me to learn more
about the other available tools in the ACTS Toolkit.