LTC Donald A. Outing
Director Contact: Office:
235B Thayer Hall Phone:
- Currently teaching MA153, Advanced Multivariable Calculus and MA484, Partial Differential Equations (Fall 2009)
- Precalculus, Differential Calculus, Integral Calculus, Multivariable Calculus, Mathematical Modeling, Probability and Statistics, Discrete Dynamical Systems, Engineering Mathematics
- Doctor of Philosophy, Mathematics, Rensselaer Polytechnic Institute, 2004
- Master of Science, Applied Mathematics, Rensselaer Polytechnic Institute, 1997
- Bachelor of Science, Mathematics, University of the State of New York, 1985
- United States Naval Academy, 1983
- There are no publications by this faculty member available at this time.
- Advances in asymptotic methods, computing power, and numerical algorithms have invigorated research in the analysis of wave propagation. Over the past three years, I have worked with Professor Bill Siegmann, Rensselaer Polytechnic Institute, and Dr. Michael Collins, Naval Research Laboratory, on a variety of propagation problems. My principal research area involves using parabolic equations to model sound transmission through shallow-water regions (especially with substantial changes in the propagation direction, including interactions with beaches and islands).
Parabolic Equation Method: The parabolic equation method was pioneered in the 1940s for the study of radio waves in the atmosphere. Since that time, the method has been extended to a wider class of wave phenomena, including ocean acoustics, geoacoustics, electromagnetics, and scattering problems. The method is based on factoring the wave equation into incoming and outgoing components. When one component of the wave dominates, the factored equation can be solved orders of magnitude more efficiently than the full elliptic wave equation. This is important when the scale of the computational domain is many acoustic wavelengths. A parabolic equation is efficiently solved by advancing the field in range with a marching algorithm.
Recently I successfully applied coordinate transformation techniques to problems involving sloping fluid-solid interfaces, which is considered the most important unresolved issue in the development of parabolic equations.