Research Statement

Current research interests include: (1) numerical solution of large systems of reaction-diffusion partial differential equations that arise in semiconductor process modeling, (2) mathematical methods for image processing including wavelets and nonlinear PDE filters, and (3) least squares methods, Sobolev gradients, and optimal embedding constants. My dissertation was completed in 1984 at the University of North Texas, under the direction of John Neuberger. It dealt with Sobolev gradient steepest descent for solving PDE's with nonlinear boundary conditions. An outgrowth of this work was a closed form solution for the best constant in one form of Sobolev's embedding inequality.

During 1985-89, I worked at the Microelectronics and Computer Technology Corporation in Austin and coauthored the semiconductor process simulator, PEPPER, which models diffusion, epitaxy, ion implantation, etching, and deposition. Our group developed several kinetic-based diffusion models to explain observed nonlinearities in impurity profiles in silicon. Since coming to UTSA, I have continued work on efficient numerical methods to solve these equations in 3-D. I co-authored Process, Device, and Circuit Simulation , taught several industrial short courses, and spent a semester with the Motorola Semiconductor Products Division in Austin.

Work with reaction-diffusion systems led to an interest in using mean-curvature-dependent/anisotropic-diffusion PDE's as nonlinear filters for image processing. I have several papers on the applications of these filters, as well as generalized order statistic filters, wavelets and wave packets to the problems of noise reduction and feature detection in medical imaging. In 1991 I spent a month working with the image processing group at Paris IX. In 1993 Dwayne Collins and I taught an NSF REU summer program, Wavelets and their Applications , at UTSA. Two months in 1994 were spend consulting on image processing software for NASA Lewisr.