Investigation of finite element-ABC methods for electromagnetic field simulation.

The demand for accurate characterization and design of complex, composite structures has necessitated the use of numerical techniques for their analysis. Since these structures are often not amenable to closed-form analytical expressions, numerical methods are the only recourse for analyzing these structures. However, a viable numerical method needs to be as efficient and economical as possible such that increasingly complex and large problems can be modeled with minimal computational resources. To this end, the method of finite elements in conjunction with absorbing boundary conditions (ABCs) is proposed in this thesis for solving large and complex three-dimensional problems in unbounded domains. The problem is first formulated using the variational as well as the weighted residual approach. The field variable is expanded in terms of edge-based finite elements on tetrahedra, for the sake of accurate modeling of field continuity and ease of imposing boundary conditions. Initially, the closed problem is solved by determining the eigenvalues of arbitrary, inhomogeneous metallic cavities. For the open problem, ABCs are used as boundary conditions on spherical mesh termination boundaries. The resulting matrix system is sparse symmetric and is found to converge rapidly when solved iteratively. Remarkably accurate results are obtained by placing the truncation boundary only 0.3$\lambda$ from the farthest edge of the target. In order to solve very large problems, the code is optimized on vector as well as parallel architectures like the KSR1 and the Intel iPSC/860. Near-linear speedup is obtained on the KSR1 for the computationally intensive portions of the finite element code, allowing extremely rapid solution for problems involving about half a million unknowns. Since existing ABCs were applicable on spherical mesh termination boundaries, long, thin geometries could be solved only at enormous computational cost. New ABCs enforceable on mesh termination boundaries conformal to the target are derived, allowing the target to be enclosed more tightly by the mesh truncation surface. This results in dramatic reductions in computer storage as well as solution time, leading to more efficient and accurate solutions. A completely general technique is thus presented and validated for efficiently solving unbounded domain 3D problems having arbitrary geometries and inhomogeneities.PhDElectrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/104272/1/9513320.pdfDescription of 9513320.pdf : Restricted to UM users only