Domain Decomposition Based Hybrid Methods for Solving Real-Life Electromagnetic Scattering and Radiation Problems.

Finite element (FE) method, boundary (B) and volume (V) integral equation (IE) methods are among the most popular numerical methods for solving electromagnetic (EM) scattering and radiation problems. Each of these methods has strengths and weaknesses when applied to certain types of problems. BIE methods are applicable to piecewise homogeneous structures (possibly including perfect electrically conducting (PEC) objects and surfaces). VIEs have ability to model arbitrarily inhomogeneous dielectric-only structures. Numerical solution of IEs via the method of moments has large computation and memory requirements. Often, fast Fourier transform-based methods such as adaptive integral method (AIM) are called for to accelerate their solution for practical size geometries. On the other hand, FE methods can handle both inhomogeneous dielectrics and PEC structures, and they require solution of sparse matrix systems which can be done efficiently. Recently, domain decomposition (DD) based FE methods gained popularity to solve multi-scale problems more efficiently. Despite their modeling capabilities, FE methods yield less accurate results compared to IE methods for the same level of discretization density. In this thesis a hybrid DD-FE-BI-VIE method is developed by combining all these methods to exploit their strengths and overcome their weaknesses for the solution of real-life EM problems. To accelerate the solution of the BI-VIE portion of this hybrid system a memory efficient extension of adaptive integral method (AIM) is developed by combining it with Fast Gaussian gridding (FGG), a recently proposed nonuniform fast Fourier transform algorithm. Numerical results that demonstrate the efficiency and accuracy of the AIM–FGG hybrid in comparison to a classical AIM-accelerated solver are presented. First, a high order AIM-FGG accelerated BIE solver is developed for composite dielectric and PEC structures with arbitrary surface junctions. Then, a hybrid DD-FE-BI solver and a VIE solver are independently developed and accelerated with AIM-FGG. Various numerical examples that validate and demonstrate the accuracy of these solvers are presented in the thesis. Finally, the solvers are combined in a hybrid DD-FE-BI-VIE solver accelerated with AIM-FGG, and preliminary results are presented to validate the solver.PhDElectrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/93907/1/onurb_1.pd