Weak Galerkin Modeling of Wave Scattering and Propagation in Dispersive Media

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The propagation and scattering of electromagnetic waves in dispersive and inhomogeneous media are of essential importance in microwave, THz (tera-hertz) and light-wave technologies. The effects of dispersive dielectrics, such as biological tissues, rocks, soil, snow, ice, plasma, optical fibers, and radar-absorbing materials, must be taken into account in the design of electromagnetic devices. The understanding of these effects leads to new devices with unique characteristics. Due to geometric complexity, interface discontinuities, solution singularity and time-varying nature of the solution, the development of efficient and accurate numerical methods for solving dispersive media problems remains a challenging issue in computational mathematics. The goal of this proposal is to develop a new efficient and accurate numerical method for modeling, analysis, and simulation of electromagnetic wave problems in dispersive and inhomogeneous media. In this project, the investigator will construct stable and reliable formulations based on the weak-Galerkin finite element method for handling the complex geometry, interface discontinuity and low regularity solution, and then extend the analysis to time dependent problems. New mathematical schemes will be developed based on dispersive media models and complicated coupling of field components at the dielectric interface. The proposed approaches will be applied to a number of realistic problems, including microwave breast imaging, ground penetrating radar and double negative metamaterial. Advanced computational tools developed in this project, including those for constructing efficient numerical formulation, handling complex geometries and interface discontinuities will lead to a major advance in mathematical modeling and computation of wave scattering and propagation in dispersive media.