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Title:Computational modeling and simulation of nonlinear electromagnetic and multiphysics problems
Author(s):Yan, Su
Director of Research:Jin, Jianming
Doctoral Committee Chair(s):Jin, Jianming
Doctoral Committee Member(s):Chew, Weng Cho; Kudeki, Erhan; Aluru, Narayana
Department / Program:Electrical & Computer Eng
Discipline:Electrical & Computer Engr
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):Nonlinear Electromagnetic Problems
Multiphysics Problems
Multiscale Problems
Time-Domain Simulation
Newton's Method
Jiles-Atherton Model
Hysteresis Model
Nonuniform Time-Stepping Scheme
Time-Domain Finite Element Method (TDFEM)
Discontinuous Galerkin Time-Domain (DGTD) Method
Local Discontinuous Galerkin (LDG) Method
High-Power Microwave (HPM)
Dielectric Breakdown
Air Breakdown
Electromagnetic--Plasma Interaction
Boltzmann's Equation
Nonlinear Conductivity
Plasma Fluid Model
Plasma Formation
Plasma Shielding
Hyperbolic Equation
Diffusion Equation
Divergence Cleaning Technique
Purely Hyperbolic Maxwell Equations
Damped Hyperbolic Maxwell Equations
Continuity Preserving
Dynamic h-Adaptation Algorithm
Dynamic p-Adaptation Algorithm
Adaptive Cartesian Mesh
Local Time-Stepping
Abstract:In this dissertation, nonlinear electromagnetic and multiphysics problems are modeled and simulated using various three-dimensional full-wave methods in the time domain. The problems under consideration fall into two categories. One is nonlinear electromagnetic problems with the nonlinearity embedded in either the permeability or the conductivity of the material's constitutive properties. The other is multiphysics problems that involve interactions between electromagnetic and other physical phenomena. A numerical solution of nonlinear magnetic problems is formulated using the three-dimensional time-domain finite element method (TDFEM) combined with the inverse Jiles-Atherton vector hysteresis model. A second-order nonlinear partial differential equation (PDE) that governs the nonlinear magnetic problem is constructed through the magnetic vector potential in the time domain, which is solved by applying the Newton-Raphson method. To solve the ordinary differential equation (ODE) representing the magnetic hysteresis accurately and efficiently, several ODE solvers are specifically designed and investigated. To improve the computational efficiency of the Newton-Raphson method, the multi-dimensional secant methods are incorporated in the nonlinear TDFEM solver. A nonuniform time-stepping scheme is also developed using the weighted residual approach to remove the requirement of a uniform time-step size during the simulation. Breakdown phenomena during high-power microwave (HPM) operation are investigated using different physical and mathematical models. During the breakdown process, the bound charges in solid dielectrics and air molecules break free and are pushed to move by the Lorentz force produced by the electromagnetic fields. The motion of free electrons produces plasma currents, which generate secondary electromagnetic fields that couple back to the externally applied fields and interact with the free electrons. When the incident field intensity is high enough, this will lead to an exponential increase of the charged particles known as breakdown. Such a process is first described by a nonlinear conductivity of the solid dielectric as a function of the electric field to model the dielectric breakdown phenomenon. The air breakdown problem encountered with HPM operation is then simulated with the plasma current modeled by a simplified plasma fluid equation. Both the dielectric and air breakdown problems are solved with the TDFEM together with a Newton's method, where the dielectric breakdown is treated as a pure nonlinear electromagnetic problem, while the air breakdown is treated as a multiphysics problem. To describe the plasma behavior more accurately, the plasma density and velocity are modeled by the equations of diffusion and motion, respectively. This results in a multiphysics and multiscale system depicted by the nonlinearly coupled full-wave Maxwell and plasma fluid equations, which are solved by a nodal discontinuous Galerkin time-domain (DGTD) method in three dimensions. The air breakdown during the HPM operation and the resulting plasma formation and shielding are modeled and simulated. Several important numerical issues in the simulation of nonlinear electromagnetic and multiphysics problems have been investigated and discussed. A continuity-preserving and divergence-cleaning scheme for electromagnetic problems involving inhomogeneous materials has been proposed based on the purely and damped hyperbolic Maxwell equations. A divergence-cleaning method is presented to enforce Gauss's laws and normal flux continuity by introducing auxiliary variables and damping terms into the original Maxwell's equations, which result in artificial propagation and dissipation of the numerical errors. Based on the DGTD method, dynamic h- and p-adaptation algorithms are developed for a full-wave analysis of electromagnetic and multiphysics problems. The dynamic h-adaptation algorithm can dynamically refine the mesh to resolve the local variation of the fields during the wave propagation, while the dynamic p-adaptation algorithm can determine and adjust the basis order in real time during the simulation. Both algorithms developed and investigated in this dissertation are highly flexible and efficient, and are powerful simulation tools in the solution of nonlinear electromagnetic and multiphysics problems.
Issue Date:2016-06-22
Rights Information:Copyright 2016 Su Yan
Date Available in IDEALS:2016-11-10
Date Deposited:2016-08

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