Time Domain Numerical Methods for Electromagnetic Wave Propagation Problems in Complex Dispersive Dielectrics

Oregon State University, Corvallis OR

Investigators

Abstract

This project aims to develop and analyze efficient numerical methods for forward problems in the time domain involving the propagation and scattering of electromagnetic waves in complex dielectric media that display physical dispersion due to multiple polarization mechanisms. The forward solution of dispersive, time-dependent electromagnetic wave systems is often used to obtain safety standards regarding exposure of humans to high-energy electromagnetic fields. These numerical simulations can also be utilized in an inverse-problem formulation, for example, in cancer detection. In imaging for medical applications, one seeks to investigate the internal structure of an object (the human body) by means of electromagnetic fields at sub-infrared frequencies to detect and characterize cancer or other anomalies by studying changes in the dielectric properties (such as permittivity, conductivity, relaxation times, etc.) of tissues. Electromagnetic wave propagation in complex dispersive media is governed by the time-dependent Maxwell's equations coupled to equations that describe the evolution of the induced macroscopic polarization. The behavior of the media's macroscopic polarization may include first-order relaxation mechanisms of Debye type, used in modeling polar materials such as water and living tissue, as well as second-order mechanisms of Lorentz type. These two mechanisms will be used as model problems. The investigator and a graduate student will develop operator-splitting techniques along with mixed finite element methods for electromagnetic wave propagation in dispersive dielectrics. Additionally, fictitious domain methods will be applied to wave-scattering problems in these materials. Efficient absorbing layers for terminating computational boundaries involving dispersive dielectrics will be constructed and analyzed. Analysis of well-posedness, stability, and convergence of the new methods will be conducted. The graduate student will study existing simulation methods and make comparisons with the newly developed computational techniques.