A Novel Approach for the Efficient Computation of 1-D and 2-D Summations

Download

index.pdf

Date

2016-03-01

Author

Karabulut, E. Pinar
ERTÜRK, VAKUR BEHÇET
Alatan, Lale
Karan, S.
Alisan, Burak
Aksun, M. I.

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

254
views

0
downloads

A novel computational method is proposed to evaluate 1-D and 2-D summations and integrals which are relatively difficult to compute numerically. The method is based on applying a subspace algorithm to the samples of partial sums and approximating them in terms of complex exponentials. For a convergent summation, the residue of the exponential term with zero complex pole of this approximation corresponds to the result of the summation. Since the procedure requires the evaluation of relatively small number of terms, the computation time for the evaluation of the summation is reduced significantly. In addition, by using the proposed method, very accurate and convergent results are obtained for the summations which are not even absolutely convergent. The efficiency and accuracy of the method are verified by evaluating some challenging 1-D and 2-D summations and integrals.

Subject Keywords

Acceleration techniques, Cylindrically stratified media, Green’s functions, Numerical methods, Periodic structure, Planar layered structure, Sommerfeld integrals

URI

https://hdl.handle.net/11511/32890

Journal

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION

DOI

https://doi.org/10.1109/tap.2016.2521860

Collections

Department of Electrical and Electronics Engineering, Article

Suggestions

OpenMETU
Core

Efficient Computation of Green's Functions for Multilayer Media in the Context of 5G Applications Mittra, Raj; Özgün, Özlem; Li, Chao; Kuzuoğlu, Mustafa (2021-03-22) This paper presents a novel method for effective computation of Sommerfeld integrals which arise in problems involving antennas or scatterers embedded in planar multilayered media. Sommerfeld integrals that need to be computed in the evaluation of spatial-domain Green's functions are often highly oscillatory and slowly decaying. For this reason, standard numerical integration methods are not efficient for such integrals, especially at millimeter waves. The main motivation of the proposed method is to comput...
An Efficient Numerical Approach for Evaluating Sommerfeld Integrals Arising in the Construction of Green's Functions for Layered Media Özgün, Özlem; Mittra, Raj; Kuzuoğlu, Mustafa (2022-01-01) This paper presents an efficient approach for evaluating the Sommerfeld integrals in the spectral domain, whose integrands typically show an oscillatory and slowly decaying behavior at high frequencies, e.g., in the millimeter wave regime. It is well known that these integrals arise in the representations of the dyadic Green's functions of layered media and efficient computation of these Green's functions is key to rapid CEM modeling of patch antennas and printed circuits designed for 5G appli...
A Non-Galerkin Spatial-Domain Approach for Efficient Calculation of the Dispersion Characteristics of Microstrip Lines Guedue, Tamer; Alatan, Lale (2008-07-11) In the analysis of dispersion characteristics of microstrip lines, spectral domain approaches has been preferred as opposed to the spatial domain calculations since the spatial domain Green's functions corresponding to the microstrip structure require the numerical evaluation of inverse Fourier transform integrals which are computationally expensive. However as demonstrated in Bernal, J. et al, (2000), the discrete complex image representation of the spatial domain Greenpsilas functions eliminates the need ...
An Efficient Semianalytical Method for Hypersingularity Treatment Over Curved Patches Selcuk, G.; Koç, Seyit Sencer (2017-05-01) In this communication, we propose an efficient method to evaluate hypersingular integrals defined on curved surfaces. First an exact expression for hypersingular kernel is derived by projecting the integral on curvilinear element on a flat surface. Next singularity subtraction employed, where the singular core is hypersingular and the remaining part is weakly singular. The singular core is evaluated analytically using finite part interpretation and the remaining weakly singular part is evaluated numerically...
A Novel Computational Method to Calculate Nonlinear Normal Modes of Complex Structures Samandarı, Hamed; Ciğeroğlu, Ender (2019-01-31) In this study, a simple and efficient computational approach to obtain nonlinear normal modes (NNMs) of nonlinear structures is presented. Describing function method (DFM) is used to capture the nonlinear internal forces under periodic motion. DFM has the advantage of expressing the nonlinear internal force as a nonlinear stiffness matrix multiplied by a displacement vector, where the off-diagonal terms of the nonlinear stiffness matrix can provide a comprehensive knowledge about the coupling between the mo...

Citation Formats

E. P. Karabulut, V. B. ERTÜRK, L. Alatan, S. Karan, B. Alisan, and M. I. Aksun, “A Novel Approach for the Efficient Computation of 1-D and 2-D Summations,” IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, pp. 1014–1022, 2016, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/32890.