Year of Publication
Master of Science in Electrical Engineering (MSEE)
Dr. Robert J. Adams
Computational electromagnetic modeling involves generating system matrices by discretizing integral equations and solving the resulting system of linear equations. Many methods of solving the system of linear equations exist and one such method is the factorization of the matrix using the so called local-global solution (LOGOS) modes. Computer codes to perform the discretization of the integral equations, filling of the matrix, and the subsequent LOGOS factorization have previously been developed by others. However, these codes are limited to complex double precision arithmetic only.
This thesis extends and expands the existing computer by creating a more general implementation that is able to analyze a problem not only in complex double precision but also in real double precision and both complex and real single precision. The existing code is expanded using "templates" in Fortran 90 and the resulting generic code is used test the performance of the LOGOS (both OL- and NL-LOGOS) factorization on matrices generated by discretization of the volume integral equation. As part of this effort, we demonstrate for the first time that the LOGOS factorization provides an O(N log N) complexity solution to the volume integral equation formulation of low-frequency electromagnetic problems.
Arcot, Kiran, "ISSUES RELATED TO THE NUMERICAL IMPLEMENTATION OF A SPARSE METHOD FOR THE SOLUTION OF VOLUME INTEGRAL EQUATIONS AT LOW FREQUENCIES" (2010). University of Kentucky Master's Theses. 53.