Transient analysis of closed- and open-region electromagnetic problems using higher order finite element method and method of moments in the time domain - Šekeljić, Nada J., author; Notaroš, Branislav M., advisor; Mueller, Jennifer, committee member; Reising, Steven C., committee member; Chandrasekar, V., committee member; Ilić, Milan M., committee member (Colorado State University. Libraries, 2015)
The principal objective of this dissertation is to develop computational electromagnetic (CEM) methodology and tools for modeling of closed (waveguide and cavity based) and open (radiation and scattering) electromagnetic structures in the time domain (TD), employing two CEM approaches. The first method is a novel higher order and large-domain Galerkin finite element method (FEM) for transient analysis of multiport microwave waveguide devices with arbitrary metallic and dielectric discontinuities. It is based on geometrical modeling using Lagrange interpolation generalized hexahedral elements, spatial field expansion in terms of hierarchical curl-conforming polynomial vector basis functions, time-stepping with an implicit unconditionally stable finite difference scheme using the Newmark-beta method, and mesh truncation introducing the waveguide port boundary condition. The second method is a novel spatially large-domain and temporally entire-domain method of moments (MoM) proposed for surface integral equation (SIE) modeling of 3-D conducting scatterers in the TD. The method uses higher order curved Lagrange interpolation generalized quadrilateral geometrical elements, higher order spatial current expansions based on hierarchical divergence-conforming polynomial vector basis functions, and temporal current modeling by means of orthogonal weighted associated Laguerre basis functions. It implements full temporal and spatial Galerkin testing and marching-on-in-degree (MOD) scheme for an iterative solution of the final system of spatially and temporally discretized MoM-TD equations. Numerical examples of waveguides and scatterers, modeled using flat and curved large elements in conjunction with field/current expansions of orders from 2 to 9, demonstrate excellent accuracy, efficiency, convergence, and versatility of the proposed methodologies. The results obtained by higher order TD-FEM and TD-MoM are in an excellent agreement with indirect solutions obtained from FEM and MoM analyses in the frequency domain (FD) in conjunction with discrete Fourier transform and its inverse, as well as with measurements and alternative full-wave numerical solutions in both TD and FD.
Keywords: finite element method; numerical techniques; transient response; method of moments; electromagnetic analysis; scattering