Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Department of Mathematics and Statistics

First Advisor

Aihua W. Wood, PhD.


We consider the transient, or time-domain, scattering problem of a two-dimensional overfilled cavity embedded in an impedance ground plane. This problem is a significant advancement from previous work where more simplified boundary conditions were used, which can limit the number of applications. This research supports a wide range of military applications such as the study of cavity-like structures on aircraft and vehicles. More importantly, this research helps detect the biggest threat on today's battlefield: improvised explosive devices. An important step in solving the problem is introducing an artificial boundary condition on a semicircle enclosing the cavity; this couples the fields from the infinite exterior domain to those fields inside. The problem is first discretized in time using the Newmark scheme, and at each time step, we derive the variational formulation and establish well-posedness of the problem. This sets the foundation for the finite element method used in the numerical analysis. Using both a planar and overfilled cavity model, we provide numerical results through the depictions of the scattered electric field and radar cross section of the cavities.

AFIT Designator


DTIC Accession Number