Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Department of Mathematics and Statistics

First Advisor

Aihua W. Wood, PhD.


This work examines the scattered fields produced when a transient wave is reflected from an infinite perfect electric conductor (PEC) ground plane with multiple embedded cavities. Incident and reflected waves will be decomposed into transverse magnetic to the z direction (TMz) and transverse electric to the z direction (TEz) polarizations, with primary focus given to the TMz. Cavities may be unfilled, partially filled, or fully filled with non-magnetic dielectric material and no assumptions are made regarding similarity, regularity, or periodicity. The Newmark method is used to discretize time and a variational formulation is presented for each time step. The principle outcome is to show that the variational formulation of the scalar problem is well posed. Additionally, the variational formulation is applied in a stable numerical model using the finite element-boundary integral (FE-BI) method. Interior fields are approximated using the finite element method (FEM) for each time step, then the boundary integral is applied using the appropriate Green’s function to approximate exterior scattered fields. The exterior fields for one time step provide the boundary conditions for the interior problem at the next time step. In this way, the numerical model marches through time. Various numerical experiments are run to examine the effect of coupling on aperture and external fields. Of particular interest are the differences between single-cavity and multiple-cavity solutions.

AFIT Designator


DTIC Accession Number