Computational Methods to Model Wave Phenomena: General Overview, Finite Differences, and Visualization
Led by Professor Carey Rappaport.

Friday, November 1, 2002, from 1:30 until 3:00 p.m.

[A follow-up seminar will be held on Friday, November 22, 2002 in the same time-slot]

November 1st Presentation [.pdf]

These seminars will be hosted at Northeastern University in 107 Robinson Hall,(a video studio with 20 seats) and broadcast to Boston University, Rensselaer Polytechnic Institute and the University of Puerto Rico at Mayagüez via two-way video and audio broadcast. Light refreshments will be served at Northeastern University. Seating will be limited. There are no fees for CenSSIS industry partners.

For more information or if you would like to attend these seminars, please contact Kristin Hicks at 617-373-5384 or khicks@coe.neu.edu to arrange to be included in the telecast.

SEMINAR ABSTRACT - Real-world problems involving electromagnetic or fluid waves are difficult to analyze, because exact solutions to the differential equations in a given geometry often do not exist. Computational Methods get around this problem by approximating the waves over small regions of space and combining them with simple relations. Given a computer with enough memory and power, arbitrarily large wave problems can be accurately solved. This two-part seminar will describe the basic idea behind fine scale sampling of fields and currents, which forms the common basis for the method of moments, finite element analysis, and finite differences.

Finite difference methods (FDTD and FDFD) are flexible and robust, yet they provide a simple way to study wave scattering in the time and frequency domains. These methods approximate Maxwell's partial differential equations by multi-dimensional centered difference equations in space. Since they finely discretize space, FD methods effectively capture rapid field changes, as well as intricate geometry variations, and are well suited for problems involving inhomogeneous volumes and rough boundaries. Despite their great modeling power, FD methods are relatively simple to understand intuitively and code effectively.

Another advantage of the FDTD method is the aesthetic appeal of watching the modeled transient wave progress from source to scatterer and outward, or along a transmission line. The second lecture of this series will present computed solutions to realistic problems of wave propagation in complex media. Part of this discussion will describe graphical visualization techniques (in Matlab) to best show the way polarized waves distribute and move about in complex three-dimensional space.