Electromagnetic analysis with discrete exterior calculus

The main focus of this dissertation is to implement discrete exterior calculus (DEC) in electromagnetic analysis. The problem is studied for both partial differential equation (PDE) and integral equation (IE) based approaches. A systematical treatment is proposed for various boundary conditions. With a careful implementation of the Hodge star operators, we are able to represent and solve electromagnetic PDEs properly with DEC. And a self-contained discrete electromagnetic theory is developed within this framework. The discrete version of many electromagnetic theorems are derived. Then a numerical Green's function (NGF) is introduced to incorporate DEC into integral equations. With interior surface relation formulated with NGF and exterior relation from surface integral equations (SIEs), we present an alternative solution for scattering problems with complex obstacles. This NGF is also applied to formulate the propagation relation in the near field heat transfer problem. Then, with the fluctuation dissipation theorem (FDT) discretized by DEC, we provide a comprehensive solution for the near field heat transfer problem among objects with complex material properties. Using DEC, we present a scalar \Phi and vector potential A based formulation with general Lorentz gauge to circumvent the low frequency breakdown for conventional E formulation. A set of decoupled boundary conditions is studied and numerically tested.LimitedAuthor requested closed access (OA after 2yrs) in Vireo ETD syste