Modeling of permittivity variations in stochastic computational electromagnetics

Abstract

With the evolution of 5G systems offering high data rates, major changes are required in the design approach of the components of communication systems. Furthermore, building complex electromagnetic systems at the terahertz frequency range is of particular interest to the scientific community. Transmitting and receiving electromagnetic (EM) subsystems, including antennas, RF circuits and devices, RF filters, waveguides, etc are essential building blocks of these systems. It has been observed that there is significant uncertainty in the realization of these components due to fabrication tolerance, especially at millimeter wave frequencies and above. In addition to the variations in material properties due to these, the complex nature of antenna hosting environments, excitation function and point of source feeding, affect the performance characteristics of these devices. Incorporating these uncertainties in the EM design of the above advanced systems, both in terms of mathematical formulation and computational implementation is challenging. The tolerance in the fabrication process results in variations of dielectric material properties, which affects the system response. Therefore, a proper quantification of uncertainties using an efficient numerical stochastic EM solver help deliver a robust and optimal design. In this scenario, this thesis explores developing fast and efficient numerical stochastic EM solvers by considering parameters with a statistical variation. Various uncertainty modeling algorithms are formulated, implemented, and their performance is evaluated, validated, and compared by considering different practical stochastic EM problems. Both intrusive and non-intrusive finite element methods (FEM) for uncertainty quantification (UQ) in electromagnetics have been studied extensively in this work. For this analysis, FEM is used due to its versatility in handling complex EM structures with multiple dielectric domains. EM problems are unique due to the special boundary conditions employed, the possibility o