Browsing by Subject "Fast algorithms"

Now showing 1 - 6 of 6

Open Access
Analysis of double-negative materials with surface integral equations and the multilevel fast multipole algorithm
(IEEE, 2011) Ergül O.; Gürel, Levent
We present a fast and accurate analysis of double-negative materials (DNMs) with surface integral equations and the multilevel fast multipole algorithm (MLFMA). DNMs are commonly used as simplified models of metamaterials at resonance frequencies and are suitable to be formulated with surface integral equations. However, realistic metamaterials and their models are usually very large with respect to wavelength and their accurate solutions require fast algorithms, such as MLFMA. We consider iterative solutions of DNMs with MLFMA and we investigate the accuracy and efficiency of solutions when DNMs are formulated with two recently developed formulations, namely, the combined tangential formulation (CTF) and the electric and magnetic current combined-field integral equation (JMCFIE). Numerical results on canonical objects are consistent with previous results in the literature on ordinary objects. © 2011 IEEE.
Open Access
Fast algorithms for large 3-D electromagnetic scattering and radiation problems
(1997) Şendur, İbrahim Kürşat
Some interesting real-life radiation and scattering problems are electrically very large and cannot be solved using traditional solution algorithms. Despite the difficulties involved, the solution of these problems usually offer valuable results that are immediately useful in real-life applications. The fast multipole method (FMM) enables the solution of larger problems with existing computational resources by reducing the computational complexity and the memory requirement of the solution without sacrificing the accuracy. This is achieved by replacing the matrix-vector multiplications of O(N^) complexity by a faster equivalent of complexity in each iteration of an iterative scheme. Fast Far-Field Algorithm(FAFFA) further reduces 0{N^) complexity to 0{N^·^). A direct solution would require 0{N^) operations.
Open Access
Fast and accurate algorithms for quadratic phase integrals in optics and signal processing
(SPIE, 2011) Koç, A.; Özaktaş, Haldun M.; Hesselink L.
The class of two-dimensional non-separable linear canonical transforms is the most general family of linear canonical transforms, which are important in both signal/image processing and optics. Application areas include noise filtering, image encryption, design and analysis of ABCD systems, etc. To facilitate these applications, one need to obtain a digital computation method and a fast algorithm to calculate the input-output relationships of these transforms. We derive an algorithm of NlogN time, N being the space-bandwidth product. The algorithm controls the space-bandwidth products, to achieve information theoretically sufficient, but not redundant, sampling required for the reconstruction of the underlying continuous functions. © 2011 SPIE.
Open Access
Fast and accurate linear canonical transform algorithms
(IEEE, 2015) Özaktaş, Haldun M.; Koç, A.
Linear canonical transforms are encountered in many areas of science and engineering. Important transformations such as the fractional Fourier transform and the ordinary Fourier transform are special cases of this transform family. This family of transforms is especially important for the modelling of wave propagation. It has many applications such as noise removal, image encryption, and analysis of optical systems. Here we discuss algorithms for fast and accurate computation of these transforms. These algorithms can achieve the same accuracy and speed as fast Fourier transform algorithms, so that they can be viewed as optimal algorithms. Efficient sampling of signals plays an important part in the development of these algorithms.
Open Access
Generalization of time-frequency signal representations to joint fractional Fourier domains
(IEEE, 2005-09) Durak, L.; Özdemir, A. K.; Arıkan, Orhan; Song, I.
The 2-D signal representations of variables rather than time and frequency have been proposed based on either Hermitian or unitary operators. As an alternative to the theoretical derivations based on operators, we propose a joint fractional domain signal representation (JFSR) based on an intuitive understanding from a time-frequency distribution constructing a 2-D function which designates the joint time and frequency content of signals. The JFSR of a signal is so designed that its projections on to the defining joint fractional Fourier domains give the modulus square of the fractional Fourier transform of the signal at the corresponding orders. We derive properties of the JFSR including its relations to quadratic time-frequency representations and fractional Fourier transformations. We present a fast algorithm to compute radial slices of the JFSR.
Open Access
The solution of large-scale electromagnetic problems with MLFMA on Single-GPU systems
(2022-01) Erkal, Mehmet Fatih
Advancements in computer technology introduce many new hardware infrastructures with high-performance processing powers. In recent years, the graphics processing unit (GPU) has been one of the popular choices that have been being used in computational engineering fields because of its massively parallel processing capacity and its easy coding structure compatible with new programming systems. The full-wave solution of large-scale electromagnetic (EM) scattering problems with traditional methods has very dense computational operations, and thus additional hardware accelerations become an indispensable demand, especially for practical and industrial applications. In this context, the GPU implementation of full-wave electromagnetic solvers such as multi-level fast multiple algorithm (MLFMA) has shown a trend in the literature for the last decade. However, the GPUs also have many restrictions and bottlenecks when implementing large-scale EM scattering problems with full-wave solvers. Limited random-access-memory (RAM) capacities and data transmission delays are the major bottlenecks. In this study, we propose a matrix partitioning scheme to overcome the RAM restriction of GPUs to be able to solve electrically large size problems in single-GPU systems with MLFMA while acquiring reasonable accelerations by considering different implementation approaches. For this purpose, the Single-Instruction-Multiple-Data (SIMD) structure of GPU is considered for each stage of the MLFMA to check its compatibility. In addition, different operators of MLFMA are fine-tuned on the GPU scale to minimize the overall effect of data transfer and device latency. The preliminary analyses show that significant time efficiencies can be obtained for the different parts of MLFMA as well as eliminating the RAM restriction. The numerical results demonstrate the overall efficiencies of our proposed solution for the bottlenecks of GPU and also validate the expected accelerations for the solution of large-scale EM problems involving electrically large canonical geometries and real-life targets such as an aircraft and a missile geometry.