Browsing by Subject "Fast multipole method (FMM)"

Now showing 1 - 4 of 4

Open Access
Error control of multiple-precision MLFMA
(Institute of Electrical and Electronics Engineers, 2018) Kalfa, M.; Ergül, Ö.; Ertürk, Vakur
We introduce and demonstrate a new error control scheme for the computation of far-zone interactions in the multilevel fast multipole algorithm when implemented within a multiple-precision arithmetic framework. The proposed scheme provides the optimum truncation numbers as well as the machine precisions given the desired relative error thresholds and the box sizes for the translation operator at all frequencies. In other words, unlike the previous error control schemes which are valid only for high-frequency problems, the proposed scheme can be used to control the error across both low- A nd high-frequency problems. Optimum truncation numbers and machine precisions are calculated for a wide range of box sizes and desired relative error thresholds with the proposed error control scheme. The results are compared with the previously available methods and numerical surveys.
Open Access
Fast multipole method for the solution of electromagnetic scattering problems
(2003) Ergül, Özgür Salih
The fast multipole method (FMM) is investigated in detail for the solution of electromagnetic scattering problems involving arbitrarily shaped three-dimensional conducting surfaces. This method is known to reduce the computational complexity and the memory requirement of the solution without sacrificing the accuracy. Therefore, it achieves the solution of large problems with less computational resources compared to the other traditional solution algorithms. However, the expected efficiency of the FMM may not be obtained unless the appropriate choices of the components are made. The types of the employed integral equation, iterative algorithm, and preconditioning technique directly affect the efficiency of the implementations. Performances of these components are also related to each other, and their simultaneous optimization creates a challenging task in the design of an efficient solver.
Open Access
Iterative near-field preconditioner for the multilevel fast multipole algorithm
(Society for Industrial and Applied Mathematics, 2010-07-06) Gürel, Levent; Malas, T.
For iterative solutions of large and difficult integral-equation problems in computational electromagnetics using the multilevel fast multipole algorithm (MLFMA), preconditioners are usually built from the available sparse near-field matrix. The exact solution of the near-field system for the preconditioning operation is infeasible because the LU factors lose their sparsity during the factorization. To prevent this, incomplete factors or approximate inverses can be generated so that the sparsity is preserved, but at the expense of losing some information stored in the near-field matrix. As an alternative strategy, the entire near-field matrix can be used in an iterative solver for preconditioning purposes. This can be accomplished with low cost and complexity since Krylov subspace solvers merely require matrix-vector multiplications and the near-field matrix is sparse. Therefore, the preconditioning solution can be obtained by another iterative process, nested in the outer solver, provided that the outer Krylov subspace solver is flexible. With this strategy, we propose using the iterative solution of the near-field system as a preconditioner for the original system, which is also solved iteratively. Furthermore, we use a fixed preconditioner obtained from the near-field matrix as a preconditioner to the inner iterative solver. MLFMA solutions of several model problems establish the effectiveness of the proposed nested iterative near-field preconditioner, allowing us to report the efficient solution of electric-field and combined-field integral-equation problems involving difficult geometries and millions of unknowns.
Open Access
Solution of radiation problems using the fast multipole method
(IEEE, 1997-07) Gürel, Levent; Şendur, İbrahim Kürşat
Electromagnetic radiation problems involving electrically large radiators and reflectors are solved using the fast multipole method (FMM). The FMM enables the solution of large problems with existing computational resources by reducing the computational complexity by a faster equivalent of O(N) complexity in each iteration of an iterative scheme. Three dimensional radiation problems involving complicated geometries are modeled using arbitrary surface triangulations. Piecewise linear basis functions defined on triangular domains due to Rao, Wilton, and Glisson (RWG) basis functions are used to approximate the induced currents. Using delta-gap voltage sources and prescribed current distributions, the operations of various antennas are simulated.