Wideband Impedance Boundary Conditions for FE/DG Methods for Solving Maxwell Equations in Time Domain

• Main Author: Woyna, Irene
• Format: Others
• Language: German; en
• Published: 2014
• Online Access: https://tuprints.ulb.tu-darmstadt.de/4008/1/main.pdf; Woyna, Irene <http://tuprints.ulb.tu-darmstadt.de/view/person/Woyna=3AIrene=3A=3A.html> (2014): Wideband Impedance Boundary Conditions for FE/DG Methods for Solving Maxwell Equations in Time Domain.Darmstadt, Technische Universität, [Ph.D. Thesis]

In this work, dispersive surface impedance boundary conditions are applied to Discontinuous Galerkin Method (DG-FEM) in the time and frequency domains, on a wide frequency band. Three different kinds of surface impedance boundary conditions are considered, namely Standard Impedance Boundary Condition (SIBC) for modeling smooth conductor surfaces with high conductivity, Corrugated Surface Boundary Condition (CSBC) for modeling corrugated conducting surfaces, and Impedance Transmission Boundary Condition (ITBC) for modeling electrically thin conductive sheets. Two different schemes for modeling dispersive surface impedance boundary conditions on a wide frequency band are presented, one in the frequency domain, and another in the time domain. In the frequency domain, a procedure for solving a complex nonlinear eigenvalue problem (EVP) arising from applying the dispersive impedance boundary conditions to the discrete Maxwell’s equations, is presented. The procedure is based on fixed point iteration, and it enables to solve for the nonlinear EVP as a linear EVP, and therefore to simplify the computational task significantly. In the time domain scheme, the dispersive boundary conditions are first approximated in the frequency domain as series of rational functions, and then transformed into the time domain by means of Laplace transform. The time stepping schemes for time domain simulations are obtained by means of Recursive Convolution (RC) and Auxiliary Differential Equation (ADE) methods. The frequency domain scheme, as well as the time domain scheme, are verified and validated by investigating the Q factors and the fundamental frequencies of different resonant structures. Numerical examples are given, and convergence studies are performed. The results are compared with the analytical results, as well as results obtained by commercial softwares. The developed schemes appear to be computationally efficient, and the accuracy very high, already with coarse meshes and low basis function orders.