University Events

Description: Topic: Spatial Frequency Analysis of Electromagnetic Scattering and Radiation

Location: Claire T. Carney Library, Room 314

Abstract:
Electromagnetic scattering and radiation is traditionally analyzed by solving Maxwell's equations and applying the pertinent boundary conditions in the spatial domain. In the spatial domain, the solution to Maxwell's equations reduces to an integral equation which is used to relate the scattered (or radiated) fields to the induced currents. Generally, complex scattering problems are solved by discretizing the integral equation and solving the resulting matrix equation to find the unknown induced currents. This spatial domain approach is referred to as the Method of Moments where the unknown currents are found for a set of known incident fields by inverting a matrix equation. The spatial domain form of the matrix equation represents a spatial convolution of the induced currents and a kernel (also known as the Green's function) derived from Maxwell's equations. As the scattering objects become larger the matrix inversion becomes computationally challenging. In recent years, there has been significant research done in reducing the computational complexity of the scattering problems by transforming the spatial domain equations into other domains which make the matrix inversion process computationally more tractable. Since the matrix equation represents a convolution, it may be transformed into a multiplication operation in the spatial frequency domain. In discrete form, a standard convolution operation yields a Toeplitz matrix in the spatial domain. A Toeplitz matrix does not automatically get transformed into a diagonal matrix in the spatial frequency domain. The Toeplitz matrix needs to be converted to an equivalent circulant matrix before being transformed into the spatial frequency domain. Circulant matrices yield diagonal matrices when transformed to the spatial frequency domain. However, converting the original Toeplitz matrix to a circulant matrix without modifying the original current/field relationship results in an expansion of the domain. The expanded domain will include the scattering surface and a corresponding complementary space. The focus of the proposed research is to investigate these issues arising from the transformation into the spatial frequency domain. Preliminary results indicate that the spatial frequency approach can speed up the matrix inversion process. A fast iterative algorithm which utilizes the multiplicative properties of the spatial frequency domain approach and the Fast Fourier Transform (FFT) algorithm has been developed for scattering from one-dimensional objects. In the proposed research, this technique will be expanded and applied to scattering from two- and three-dimensional canonical objects. Another objective of this project is to analyze and formulate the properties of the complementary space in order to further speed up the spatial frequency domain matrix inversion process.

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

Advisor: Dr. Dayalan Kasilingam
Committee Members: Dr. Paul J. Gendron and Dr. Karen L. Payton, Department of Electrical & Computer Engineering, University of Massachusetts Dartmouth; Dr. Gaurav Khanna, Physics Department, University of Massachusetts Dartmouth; Dr. Sadasiva M. Rao, Naval Research Laboratory

*For further information, please contact Dr. Dayalan P. Kasilingam at 508.999.8534, or via email at dkasilingam@umassd.edu.