Büyük ölçekli yüzey integral denklemi problemlerinin iteratif çözümleri için etkin öniyileştiriciler

A popular method to study electromagnetic scattering and radiation of threedimensionalelectromagnetics problems is to solve discretized surface integralequations, which give rise to dense linear systems. Iterative solution of suchlinear systems using Krylov subspace iterative methods and the multilevel fastmultipole algorithm (MLFMA) has been a very attractive approach for largeproblems because of the reduced complexity of the solution. This scheme workswell, however, only if the number of iterations required for convergence of theiterative solver is not too high. Unfortunately, this is not the case for manypractical problems. In particular, discretizations of open-surface problems andcomplex real-life targets yield ill-conditioned linear systems. The iterative solutionsof such problems are not tractable without preconditioners, which can beroughly defined as easily invertible approximations of the system matrices.In this dissertation, we present our efforts to design effective preconditioners forlarge-scale surface-integral-equation problems. We first address incomplete LU(ILU) preconditioning, which is the most commonly used and well-establishedpreconditioning method. We show how to use these preconditioners in a blackboxform and safe manner. Despite their important advantages, ILU preconditionersare inherently sequential. Hence, for parallel solutions, a sparseapproximate-inverse (SAI) preconditioner has been developed. We propose anovel load-balancing scheme for SAI, which is crucial for parallel scalability.Then, we improve the performance of the SAI preconditioner by using it for theiterative solution of the near-field matrix system, which is used to preconditionthe dense linear system in an inner-outer solution scheme. The last preconditionerwe develop for perfectly-electric-conductor (PEC) problems uses the sameinner-outer solution scheme, but employs an approximate version of MLFMA forinner solutions. In this way, we succeed to solve many complex real-life problemsincluding helicopters and metamaterial structures with moderate iteration countsand short solution times. Finally, we consider preconditioning of linear systemsobtained from the discretization of dielectric problems. Unlike the PEC case,those linear systems are in a partitioned structure. We exploit the partitionedstructure for preconditioning by employing Schur complement reduction. In thisway, we develop effective preconditioners, which render the solution of difficultreal-life problems solvable, such as dielectric photonic crystals.