Domain Decomposition Methods for Finite Periodic Structures in Electromagnetics

Abstract: Long computational times persist on being a limiting factor when designing complex electromagnetic structures. Even though computers get more and more powerful, the most efficient improvement for reducing the necessary time when solving a numerical problem is to change or optimise the used numerical method. One numerical method introduced lately is the domain decomposition method (DDM). This thesis explores the available algorithms for computational electromagnetics which are based on DDM. The study is concentrated on algorithms available for computational electromagnetics. The aim of the study is to find and further study one appropriate method for analysing finite periodic electromagnetic structures like frequency selective surfaces and array antennas. After an introducing study of DDM, the FACTOPO method, is selected and studied in detail. The study includes an implementation of the method, which is performed in three versions. The first deals with a 1-Dimensional waveguide problem which follows the FACTOPO method for determining the scattering parameters of a subdomain using admittance parameters of the corresponding domain. By limiting the subdomain with perfect electric conductor (PEC) the computational problem is efficiently reduced. The second implementation continues to explore the 1-Dimensional problem but introduces the ability of importing scattering parameters of a specific domain from an electromagnetic simulation software. The third, and last, implementation is an extension of the second version which introduces a 2-D structure based on a 4-port unit cell. The theoretical study and the results from the implementation show that that domain decomposition is a promising numerical technique which, when used properly, can improve the numerical simulation software for electromagnetic structures. It is also concluded that domain decomposition is especially promising for periodic electromagnetic structures.