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Dissertation Defense

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

Onur Bakir

: Finite element (FE) method, boundary (B) and volume (V) integral equation (IE) methods are among the most popular numerical methods for solving electromagnetic scattering and radiation problems. Recently, domain decomposition (DD) based FE methods gained popularity to solve multi-scale problems more efficiently. However, each of these methods has strengths and weaknesses when applied to certain types of problems. 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. 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. 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 demonstrate the accuracy and efficiency 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.

Sponsored by

Eric Michielssen