• About
  • Policies
  • What is openaccess
  • Library
  • Contact
Advanced search
      View Item 
      •   BUIR Home
      • University Library
      • Bilkent Theses
      • Theses - Department of Electrical and Electronics Engineering
      • Dept. of Electrical and Electronics Engineering - Ph.D. / Sc.D.
      • View Item
      •   BUIR Home
      • University Library
      • Bilkent Theses
      • Theses - Department of Electrical and Electronics Engineering
      • Dept. of Electrical and Electronics Engineering - Ph.D. / Sc.D.
      • View Item
      JavaScript is disabled for your browser. Some features of this site may not work without it.

      Effective preconditioners for iterative solutions of large-scale surface-integral-equation problems

      Thumbnail
      View / Download
      5.2 Mb
      Author
      Malas, Tahir
      Advisor
      Gürel, Levent
      Date
      2010
      Publisher
      Bilkent University
      Language
      English
      Type
      Thesis
      Item Usage Stats
      32
      views
      16
      downloads
      Metadata
      Show full item record
      Abstract
      A 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.
      Keywords
      Preconditioning
      incomplete-LU preconditioners
      sparse-approximateinverse preconditioners
      flexible solvers
      variable preconditioning
      computational electromagnetics
      surface integral equations
      multilevel fast multipole algorithm
      electromagnetic scattering
      parallel computing
      Permalink
      http://hdl.handle.net/11693/15432
      Collections
      • Dept. of Electrical and Electronics Engineering - Ph.D. / Sc.D. 136

      Browse

      All of BUIRCommunities & CollectionsTitlesAuthorsAdvisorsBy Issue DateKeywordsTypeDepartmentsThis CollectionTitlesAuthorsAdvisorsBy Issue DateKeywordsTypeDepartments

      My Account

      Login

      Statistics

      View Usage Statistics

      Bilkent University

      If you have trouble accessing this page and need to request an alternate format, contact the site administrator. Phone: (312) 290 1771
      Copyright © Bilkent University | Library IT

      Contact Us | Send Feedback | Off-Campus Access | Admin