Browsing by Author "Ergül, Ö."

Now showing 1 - 8 of 8

Open Access
Broadband analysis of multiscale electromagnetic problems: Novel incomplete-leaf MLFMA for potential integral equations
(IEEE, 2021-06-24) Khalichi, Bahram; Ergül, Ö.; Takrimi, Manouchehr; Ertürk, Vakur B.
Recently introduced incomplete tree structures for the magnetic-field integral equation are modified and used in conjunction with the mixed-form multilevel fast multipole algorithm (MLFMA) to employ a novel broadband incomplete-leaf MLFMA (IL-MLFMA) to the solution of potential integral equations (PIEs) for scattering/radiation from multiscale open and closed surfaces. This population-based algorithm deploys a nonuniform clustering that enables to use deep levels safely and, when necessary, without compromising the accuracy resulting in an improved efficiency and a significant reduction for the memory requirements (order of magnitudes), while the error is controllable. The superiority of the algorithm is demonstrated in several canonical and real-life multiscale geometries.
Open Access
Broadband multilevel fast multipole algorithm for large-scale problems with nonuniform discretizations
(IEEE, 2016) Ergül, Ö.; Karaosmanoğlu, B.; Takrimi, Manouchehr; Ertürk, Vakur B.
We present a broadband implementation of the multilevel fast multipole algorithm (MLFMA) for fast and accurate solutions of multiscale problems involving highly nonuniform discretizations. Incomplete tree structures, which are based on population-based clustering with flexible leaf-level boxes at different levels, are used to handle extremely varying triangulation sizes on the same structures. Superior efficiency and accuracy of the developed implementation, in comparison to the standard and broadband MLFMA solvers employing conventional tree structures, are demonstrated on practical problems.
Open Access
A broadband multilevel fast multipole algorithm with incomplete-leaf tree structures for multiscale electromagnetic problems
(IEEE, 2016) Takrimi, Manouchehr; Ergül, Ö.; Ertürk, Vakur B.
An efficient, broadband, and accurate multilevel fast multipole algorithm (MLFMA) is proposed to solve a wide range of multiscale electromagnetic problems with orders of magnitude differences in the mesh sizes. Given a maximum RWG population threshold, only overcrowded boxes are recursively bisected into smaller ones, which leads to novel incomplete-leaf tree structures. Simulations reveal that, for surface discretizations possessing highly overmeshed local regions, the proposed method presents a more efficient and/or accurate results than the conventional MLFMA. The key feature of such a population-based clustering scenario is that the error is controllable, and hence, regardless of the number of levels, the efficiency can be optimized based on the population threshold. Numerical examples are provided to demonstrate the superior efficiency and accuracy of the proposed algorithm in comparison to the conventional MLFMA.
Open Access
Broadband solutions of potential integral equations with NSPWMLFMA
(IEEE, 2019-06) Khalichi, Bahram; Ergül, Ö.; Ertürk, Vakur B.
In this communication, a mixed-form multilevel fast multipole algorithm (MLFMA) is combined with the recently introduced potential integral equations (PIEs), also called as the A-φ system, to obtain an efficient and accurate broadband solver that can be used for the solution of electromagnetic scattering from perfectly conducting surfaces over a wide frequency range including low frequencies. The mixed-form MLFMA uses the nondirective stable planewave MLFMA (NSPWMLFMA) at low frequencies and the conventional MLFMA at middle/high frequencies. Various numerical examples are presented to assess the validity, efficiency, and accuracy of the developed solver.
Open Access
Error control in MLFMA with multiple-precision arithmetic
(Institution of Engineering and Technology, 2018-04) Kalfa, Mert; Ergül, Ö.; Ertürk, Vakur B.
We present a new error control method that provides the truncation numbers as well as the required digits of machine precision for the translation operator of the multilevel fast multipole algorithm (MLFMA). The proposed method is valid for all frequencies, whereas the previous studies on error control are valid only for high-frequency problems (i.e., electrically large translation distances). When combined with a multiple-precision implementation of MLFMA, the proposed method can be used to solve low-frequency problems that are problematic with a fixed-precision implementation. Numerical results in the form of optimal truncation numbers and machine precisions for a variety of box sizes and desired relative error thresholds are presented and compared with the methods or numerical surveys available in the literature.
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
Incomplete-leaf multilevel fast multipole algorithm for multiscale penetrable objects formulated with volume integral equations
(Institute of Electrical and Electronics Engineers Inc., 2017) Takrimi, M.; Ergül, Ö.; Ertürk, V. B.
Recently introduced incomplete-leaf (IL) tree structures for multilevel fast multipole algorithm (referred to as IL-MLFMA) is proposed for the analysis of multiscale inhomogeneous penetrable objects, in which there are multiple orders of magnitude differences among the mesh sizes. Considering a maximum Schaubert-Wilton-Glisson function population threshold per box, only overcrowded boxes are recursively divided into proper smaller boxes, leading to IL tree structures consisting of variable box sizes. Such an approach: 1) significantly reduces the CPU time for near-field calculations regarding overcrowded boxes, resulting a superior efficiency in comparison with the conventional MLFMA where fixed-size boxes are used and 2) effectively reduces the computational error of the conventional MLFMA for multiscale problems, where the protrusion of the basis/testing functions from their respective boxes dramatically impairs the validity of the addition theorem. Moreover, because IL-MLFMA is able to use deep levels safely and without compromising the accuracy, the memory consumption is significantly reduced compared with that of the conventional MLFMA. Several examples are provided to assess the accuracy and the efficiency of IL-MLFMA for multiscale penetrable objects.
Open Access
A novel broadband multilevel fast multipole algorithm with incomplete-leaf tree structures for multiscale electromagnetic problems
(Institute of Electrical and Electronics Engineers Inc., 2016) Takrimi, M.; Ergül, Ö.; Ertürk, V. B.
An efficient and versatile broadband multilevel fast multipole algorithm (MLFMA), which is capable of handling large multiscale electromagnetic problems with a wide dynamic range of mesh sizes, is presented. By invoking a novel concept of incomplete-leaf tree structures, where only the overcrowded boxes are divided into smaller ones for a given population threshold, versatility of using variable-sized boxes is achieved. Consequently, for geometries containing highly overmeshed local regions, the proposed method is always more efficient than the conventional MLFMA for the same accuracy, while it is always more accurate if the efficiency is comparable. Furthermore, in such a population-based clustering scenario, the error is controllable regardless of the number of levels. Several canonical examples are provided to demonstrate the superior efficiency and accuracy of the proposed algorithm in comparison with the conventional MLFMA. ï¿½ 2016 IEEE.