Browsing by Subject "multilevel fast multipole algorithm"

Now showing 1 - 2 of 2

Open Access
Effective preconditioners for iterative solutions of large-scale surface-integral-equation problems
(2010) Malas, Tahir
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.
Open Access
Out-of-core implementation of the parallel multilevel fast multipole algorithm
(2013) Karaosmanoğlu, Barışcan
We developed an out-of-core (OC) implementation of the parallel multilevel fast multipole algorithm (MLFMA) to solve electromagnetic problems with reduced memory. The main purpose of the OC method is to reduce in-core memory (primary storage) by using mass storage (secondary storage) units. Depending on the OC implementation, the in-core data may be left in one piece or divided into partitions. If the latter, the partitions are written out into mass storage unit(s) and read into in-core memory when required. In this way, memory reduction is achieved. However, the proposed method causes time delays because reading and writing large data using massive storage units is a long procedure. In our case, repetitive access to data partitions from the mass storage increases the total time of the iterative solution part of MLFMA. Such time delays can be minimized by selecting the right data type and optimizing the sizes of the data partitions. We run the optimization tests on different types of mass storage devices, such as hard disks and solid state drives. This thesis explores OC implementation of the parallel MLFMA. To be more precise, it presents the results of optimization tests done on different partition sizes and shows how computation time is minimized despite the time delays. This thesis also presents full-wave solutions of scattering problems including hundreds of millions of unknowns by employing an OC-implemented parallel MLFMA.