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dc.contributor.advisorGürel, Levent
dc.contributor.authorMalas, Tahir
dc.date.accessioned2016-01-08T18:18:25Z
dc.date.available2016-01-08T18:18:25Z
dc.date.issued2010
dc.identifier.urihttp://hdl.handle.net/11693/15432
dc.descriptionAnkara : The Department of Electrical and Electronics Engineering and the Institute of Engineering and Sciences of Bilkent University, 2010.en_US
dc.descriptionThesis (Ph.D.) -- Bilkent University, 2010.en_US
dc.descriptionIncludes bibliographical references leaves 171-187.en_US
dc.description.abstractA popular method to study electromagnetic scattering and radiation of threedimensional electromagnetics problems is to solve discretized surface integral equations, which give rise to dense linear systems. Iterative solution of such linear systems using Krylov subspace iterative methods and the multilevel fast multipole algorithm (MLFMA) has been a very attractive approach for large problems because of the reduced complexity of the solution. This scheme works well, however, only if the number of iterations required for convergence of the iterative solver is not too high. Unfortunately, this is not the case for many practical problems. In particular, discretizations of open-surface problems and complex real-life targets yield ill-conditioned linear systems. The iterative solutions of such problems are not tractable without preconditioners, which can be roughly defined as easily invertible approximations of the system matrices. In this dissertation, we present our efforts to design effective preconditioners for large-scale surface-integral-equation problems. We first address incomplete LU (ILU) preconditioning, which is the most commonly used and well-established preconditioning method. We show how to use these preconditioners in a blackbox form and safe manner. Despite their important advantages, ILU preconditioners are inherently sequential. Hence, for parallel solutions, a sparseapproximate-inverse (SAI) preconditioner has been developed. We propose a novel load-balancing scheme for SAI, which is crucial for parallel scalability. Then, we improve the performance of the SAI preconditioner by using it for the iterative solution of the near-field matrix system, which is used to precondition the dense linear system in an inner-outer solution scheme. The last preconditioner we develop for perfectly-electric-conductor (PEC) problems uses the same inner-outer solution scheme, but employs an approximate version of MLFMA for inner solutions. In this way, we succeed to solve many complex real-life problems including helicopters and metamaterial structures with moderate iteration counts and short solution times. Finally, we consider preconditioning of linear systems obtained from the discretization of dielectric problems. Unlike the PEC case, those linear systems are in a partitioned structure. We exploit the partitioned structure for preconditioning by employing Schur complement reduction. In this way, we develop effective preconditioners, which render the solution of difficult real-life problems solvable, such as dielectric photonic crystals.en_US
dc.description.statementofresponsibilityMalas, Tahiren_US
dc.format.extentxxiii, 187 leaves, tablesen_US
dc.language.isoEnglishen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectPreconditioningen_US
dc.subjectincomplete-LU preconditionersen_US
dc.subjectsparse-approximateinverse preconditionersen_US
dc.subjectflexible solversen_US
dc.subjectvariable preconditioningen_US
dc.subjectcomputational electromagneticsen_US
dc.subjectsurface integral equationsen_US
dc.subjectmultilevel fast multipole algorithmen_US
dc.subjectelectromagnetic scatteringen_US
dc.subjectparallel computingen_US
dc.subject.lccTA347.I5 M35 2010en_US
dc.subject.lcshIntegral equations.en_US
dc.subject.lcshElectromagnetic waves--Scattering.en_US
dc.titleEffective preconditioners for iterative solutions of large-scale surface-integral-equation problemsen_US
dc.typeThesisen_US
dc.departmentDepartment of Electrical and Electronics Engineeringen_US
dc.publisherBilkent Universityen_US
dc.description.degreePh.D.en_US


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