A Log-Scale Interpolation Method for Layered Medium Green's Functions

Yang, Hongfeng; Yılmaz, Ali E.

doi:10.1109/apusncursinrsm.2018.8608315

Cited by 7 publications

(4 citation statements)

References 6 publications

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“…The plane wave is applied to study the interpolation error in interpolation polynomial is given as (13) in Appendix [17,18]. The error definition and asymptotic forms of maximum and RMS errors for the first and second order interpolations are presented in [14].…”

Section: Interpolation Error Of Plane Wave In 1-dmentioning

confidence: 99%

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Error Analysis of Higher Order Bivariate Lagrange and Triangular Interpolations in Electromagnetics

Luo

Wang

et al. 2020

IEEE Open J. Antennas Propag.

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The interpolation errors of the higher order bivariate Lagrange polynomial interpolation based on the rectangular, right and equilateral triangular interpolations are measured by using the maximum and root-mean-square (RMS) errors. The error distributions of above three kinds of interpolations are analyzed to find the regions having the smallest interpolation error. Both analytical and numerical results show that the right triangular interpolation is the most efficient interpolation method. Although both the maximum and RMS errors of the right triangular interpolation are larger than that of the rectangular interpolation, the number of data points used in the triangular interpolation is up to 50% less than that used in the rectangular one. On the other hand, the equilateral triangular interpolation using the regions inside a big triangle as interpolation area is proved to be the most accurate interpolation method. The interpolation errors of the equilateral triangular are almost half of that of the rectangular interpolation. In addition, the right triangular, equilateral triangular and rectangular interpolations for the third and fourth orders are applied to accelerate the calculation of doubly periodic Green's function (PGF). Index Terms-Doubly periodic Green's function (PGF); Lagrange polynomial interpolation; maximum error; plane waves; root-mean-square (RMS) error; triangular interpolations. I. INTRODUCTION NTERPOLATION has been widely used in many areas of computational electromagnetics (CEM) to save the CPU time, e.g., the moment method, the finite element method (FEM), and so on [1-5]. Accurate and efficient evaluation of free-space periodic Green's functions (PGF) takes an important role in CEM [6, 7]. The PGF with two-dimensional (2-D) lattices is in the form of double infinite spectral and spatial summations, which is usually slowly convergent [8, 9]. For the doubly PGF,

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Section: Interpolation Error Of Plane Wave In 1-dmentioning

confidence: 99%

“…The Ewald and the Kummer's methods are two robust and efficient methods to accelerate the evaluation of PGF, which are still time consuming however [12]. Pre-calculated PGFs are applied to evaluate the PGF using the interpolation method within a certainly accuracy to reduce the CPU time [12][13][14].…”

mentioning

confidence: 99%

Error Analysis of Higher Order Bivariate Lagrange and Triangular Interpolations in Electromagnetics

Luo

Wang

et al. 2020

IEEE Open J. Antennas Propag.

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“…Such Sommerfeld integrals can be numerically evaluated by deforming the integration path in the complex k ρ plane . To improve accuracy and speed of the Green's function computations, a singularity subtraction scheme is used together with spatial interpolation in this paper: analytically integrable asymptotic forms of the spectral‐domain quantities are subtracted from the integrand; the resulting integrals are numerically evaluated, tabulated, and spatially interpolated in linear and log scales; and the interpolation results are added to analytically evaluated terms.…”

Section: Formulationmentioning

confidence: 99%

A parallel FFT‐accelerated layered‐medium integral‐equation solver for electronic packages

Liu

Aygün

Yılmaz

2019

Int J Numerical Modelling

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A parallel iterative layered‐medium integral‐equation solver is presented for fast and scalable network parameter extraction of electronic packages. The solver, which relies on a 2‐D fast Fourier transform (FFT)‐based algorithm and a sparse preconditioner to reduce computational complexity, is parallelized using three workload decomposition strategies, including a pencil decomposition that increases the scalability of the computationally dominant FFT‐based multiplication stage. A set of increasingly difficult benchmark problems, which require network parameter computations for Ntrace = 1 to 257 package‐scale interconnects, are solved on a petaflop scale computer to quantify the solver's accuracy, efficiency, and scalability. The total serialized computation time is observed to scale asymptotically as Ntrace2.6logNtrace. For the largest problem, using ~1.14 million unknowns and 1536 processes, the solver requires a wall‐clock time of ~0.05 s per iteration, ~1 minute per excitation, ~9 h per frequency, and ~424 hours to extract the 514‐port network parameters at 40 sample frequencies between 1 to 40 GHz.

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“…Genel olarak, katmanlı ortam Green fonksiyonu Sommerfeld integralini içerdiğinden, tüm gözlem ve kaynak noktaları için katmanlı ortam Green fonksiyonunu hesaplamak çok zaman alır. Bu nedenle, enterpolasyon, katmanlı ortam Green fonksiyonunun hesaplanmasında CPU süresini azaltmak için önemli bir rol oynar [33]. Yüzey integral denklemi için sistem denklemleri, katmanlı ortam Green fonksiyonları üç boyutlu (3B) olarak enterpole edildiğinde ve Kummer asimptotik (tekillik) çıkarma yöntemi ile hızlandırıldığında verimli bir şekilde elde edilebilir [34].…”

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Karmaşık objeler içeren çok katmanlı periyodik yapılardan saçılan elektromanyetik dalgaların analizi için katmanlar arası akımları kullanan verimli bir integral denklem yöntemi

Özdemir

2023

Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi

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Bu makalede, katmanlı dielektrik ortamlara gömülü, üç boyutlu (3B), elektromanyetik (EM) dalgaların geçebildiǧi objelerden oluşan çok katmanlı ikili periyodik dizilerden saçılan EM dalgaları analiz etmek için yüzey integral denklem tabanlı, verimli bir yöntem önerilmektedir. Önerilen yöntemde, katmanlar arasında bulunan arayüzlerin üzerindeki eşdeğer elektrik ve manyetik akımları tanımlamak için yüzeysel eşdeğerlik ilkesi kullanılmakta, bu sayede katmanlı dielektrik ortamlar için Green fonksiyonunu hesaplama gerekliliği ortadan kaldırılmaktadır. Arayüzler, fiziksel veya kurgusal olabilir. Arayüzlerin fiziksel olduğu durumda, belli bir katmandaki arka plan ortamı, sonsuz bir ikili periyodik dizi için Green fonksiyonu hesaplamasının yeterli olduğu homojen, iki boyutlu (2B) sınırsız bir ortam olarak kabul edilebilir. Elde edilen momentler yöntemi (MoM) etkileşim matrisi blok-tridiagonal bir yapıya sahiptir; bu ise, hem matris dolumu, hem de matris denklemi çözümü için katman sayısı bakımından doğrusal olan bir hesaplama karmaşıklığına yol açar. Önerilen yöntem yoluyla elde edilen sayısal sonuçlar, FDTD (Zaman Alanında Sonlu Farklar) tabanlı ticari yazılım kullanılarak elde edilen sonuçlarla karşılaştırılarak doğrulanmıştır.

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A Log-Scale Interpolation Method for Layered Medium Green's Functions

Cited by 7 publications

References 6 publications

Error Analysis of Higher Order Bivariate Lagrange and Triangular Interpolations in Electromagnetics

Error Analysis of Higher Order Bivariate Lagrange and Triangular Interpolations in Electromagnetics

A parallel FFT‐accelerated layered‐medium integral‐equation solver for electronic packages

Karmaşık objeler içeren çok katmanlı periyodik yapılardan saçılan elektromanyetik dalgaların analizi için katmanlar arası akımları kullanan verimli bir integral denklem yöntemi

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