Approximate Stable Diagonalization of the Green's Function for Low Frequencies

Ergül, Özgür; Karaosmanoğlu, Barışcan

doi:10.1109/lawp.2014.2327092

Cited by 22 publications

(11 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In comparison with the conventional MLFMA, the efficiency and accuracy of the proposed IL-MLFMA are revealed better as the multiscale factor increases. An approximate method for the diagonalization of Green's function proposed in [8], which is simple and demonstrated to be stable at arbitrary low-frequencies, is implemented to handle the well-known low-frequency problems of the MLFMA. However, other methods that are proposed to treat this problem [9]- [14] can also be used in conjunction with the proposed IL-MLFMA.…”

mentioning

confidence: 99%

A Novel Broadband Multilevel Fast Multipole Algorithm With Incomplete-Leaf Tree Structures for Multiscale Electromagnetic Problems

Takrimi

Ergül

Ertürk

2016

IEEE Trans. Antennas Propagat.

Self Cite

View full text Add to dashboard Cite

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.

show abstract

mentioning

confidence: 99%

A Novel Broadband Multilevel Fast Multipole Algorithm With Incomplete-Leaf Tree Structures for Multiscale Electromagnetic Problems

Takrimi

Ergül

Ertürk

2016

IEEE Trans. Antennas Propagat.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Lowfrequency issue is treated exactly the same way as discussed in [4]. The edge lengths for the triangles vary from 0.03 mm (λ/33, 300) at the front up to 7 mm (λ/142) at the back of the sphere, resulting a nonuniform mesh consisting of 210,864 Far-zone electric field scattered from a PEC sphere of radius R = 5 cm illuminated by a unit plane wave at 300 MHz.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…In comparison to the conventional MLFMA, the efficiency and accuracy of the proposed IL-MLFMA are better when the multiscale factor, defined as the ratio of the largest edge length to the smallest one over the entire meshed surface, increases. An approximate method for the diagonalization of the Green's function proposed in [4], which is simple and stable at arbitrary low-frequencies, is implemented to overcome the well-known low-frequency problem of MLFMA. The IL tree structures automatically reduce to the traditional ones and the proposed IL-MLFMA reduces into the conventional MLFMA, if desired, for uniform meshes.…”

Section: Introductionmentioning

confidence: 99%

A broadband multilevel fast multipole algorithm with incomplete-leaf tree structures for multiscale electromagnetic problems

Takrimi

Ergül

Ertürk

2016

2016 10th European Conference on Antennas and Propagation (EuCAP)

Self Cite

View full text Add to dashboard Cite

Abstract-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.Index Terms-Broadband solvers, multilevel fast multipole algorithm, incomplete leaf, multiscale problems.

show abstract

“…For example, two to three digits of accuracy (1% and 0.1% maximum relative error) using a one-box-buffer scheme need a minimum box size of around λ u . It is possible to use smaller boxes and/or to achieve higher accuracy, if alternative expansion tools [38,39], such as a direct application of multipoles [40] or evanescent waves [41], are employed. In this chapter, where numerical solutions are performed with maximum 1% error, we restrict ourselves to the plane-wave expansion.…”

Section: Matrix-vector Multiplications With Mlfmamentioning

confidence: 99%

Integral-Equation Formulations of Plasmonic Problems in the Visible Spectrum and Beyond

Çekinmez¹,

Karaosmanoğlu²,

Ergül³

2017

Dynamical Systems - Analytical and Computational Techniques

Self Cite

View full text Add to dashboard Cite

Computational modeling of nano-plasmonic structures is essential to understand their electrodynamic responses before experimental efforts in measurement setups. Similar to the other ranges of the electromagnetic spectrum, there are alternative methods for the numerical analysis of nano-plasmonic problems, while the optics literature is dominated by differential equations that require discretizations of the host media with artificial truncations. These approaches often need serious assumptions, such as periodicity, infinity, or self-similarity, in order to reduce the computational load. On the other hand, surface integral equations based on integro-differential operators can bring important advantages for accurate and efficient modeling of nano-plasmonic problems with arbitrary geometries. Electrical properties of materials, which may be obtained either experimentally or via physical modeling, can easily be inserted into integral-equation formulations, leading to accurate predictions of electromagnetic responses of complex structures. This chapter presents the implementation of such accurate, efficient, and reliable solvers based on appropriate combinations of surface integral equations, discretizations, numerical integrations, fast algorithms, and iterative techniques. As a case study, nanowire transmission lines are investigated in wide-frequency ranges, demonstrating the capabilities of the developed implementations.

show abstract

Approximate Stable Diagonalization of the Green's Function for Low Frequencies

Cited by 22 publications

References 11 publications

A Novel Broadband Multilevel Fast Multipole Algorithm With Incomplete-Leaf Tree Structures for Multiscale Electromagnetic Problems

A Novel Broadband Multilevel Fast Multipole Algorithm With Incomplete-Leaf Tree Structures for Multiscale Electromagnetic Problems

A broadband multilevel fast multipole algorithm with incomplete-leaf tree structures for multiscale electromagnetic problems

Integral-Equation Formulations of Plasmonic Problems in the Visible Spectrum and Beyond

Contact Info

Product

Resources

About