Paulo Goldfeld's Application

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.