University Events

Description: Topic: Spectral Domain Fast Multipole Method for Solving Integral Equations in Electromagnetic Wave
Scattering

Location: Lester W. Cory Conference Room, Science & Engineering Building (SENG), Room 213A

Abstract:
In this dissertation, a spectral domain implementation of the fast multipole method is presented. It is shown that the aggregation, translation, and disaggregation stages of the fast multipole method (FMM) can be performed using spectral domain (SD) analysis. FMM is a technique that is used widely to reduce the speed and memory requirements of computing the electromagnetic scattering from large objects. Calculating the electromagnetic scattering from objects requires the solution of an integral equation which relates the scattered fields to the induced currents. In the Method of Moments (MoM), the integral equation is discretized into a matrix equation. Conventional FMM uses a near field/far field separation to speed up the computation of the matrix elements. The spectral domain fast multipole method (SD-FMM) has the advantage of eliminating the near field/far field classification used in conventional FMM formulation. The goal of this study was to investigate the similarities of the spectral domain analysis and the FMM formulation. The benefits of the spectral domain analysis such as transforming the convolutional form of the Green’s function to a multiplicative form are incorporated in the SD-FMM method. The study focuses on the application of SD-FMM to one-, two- and three-dimensional electric field integral equations (EFIE). The cases of perfectly conducting (PEC) strips, circular and square perfectly conducting cylinders are numerically analyzed. For three-dimensional cases, a perfectly conductor sphere, square flat plate, and circular disk are also analyzed. The results from the SD-FMM method are compared with the results from the conventional FMM and the direct application of Method of Moments (MoM). All the results compared well with results from the direct application of MoM and FMM.

Note: All ECE Graduate Students are ENCOURAGED to attend.
All interested parties are invited to attend. Open to the public.

Advisor: dr. Dayalan P. Kasilingam
Committee Members: Dr. Antonio H. Costa and Dr. Paul J. Gendron, Department of Electrical & Computer Engineering, UMASS Dartmouth; Dr. Alfa Heryudono, Department of Mathematics, UMASS Dartmouth; Dr. Branislav M. Notaros, Department of Electrical & Computer Engineering, Colorado State University