Comparison between Specialized Quadrature Rules for Method of Moments with NURBS Modelling Applied to Periodic Multilayer Structures

A comparison between Ma-Rokhlin-Wandzura (MRW) and double exponential (DE) quadrature rules for numerical integration of method of moments (MoM) matrix entries with singular behavior is presented for multilayer periodic structures. Non Uniform Rational B-Splines (NURBS) modelling of the layout surfaces is implemented to provide high-order description of the geometry. The comparison is carried out in order to show that quadrature rule is more suitable for MoM matrix computation in terms of sampling, accuracy of computation of MoM matrix, and CPU time consumption. The comparison of CPU time consumption shows that the numerical integration with MRW samples is roughly 15 times faster than that numerical integration using DE samples for results with similar accuracies. These promising results encourage to carry out a comparison with results obtained in previous works where a specialized approach for the specific analysis of split rings geometries was carried out. This previous approach uses spectral MoM version with specific entire domain basis function with edge singularities defined on split ring geometry. Thus, the previous approach provides accurate results with low CPU time consumption to be compared. The comparison shows that CPU time consumption obtained by MRW samples is similar to the CPU time consumption required by the previous work of specific analysis of split rings geometries. The fact that similar CPU time consumptions are obtained by MRW quadrature rules for modelling of general planar geometries and by the specialized approach for split ring geometry provides an assessment for the usage of the MRW quadrature rules and NURBS modelling. This fact provides an efficient tool for analysis of reflectarray elements with general planar layout geometries, which is suitable for reflectarray designs under local periodicity assumption where a huge number of periodic multilayer structures have to be analyzed.

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Closed-Form Expressions for Numerical Evaluation of Self-Impedance Terms Involved on Wire Antenna Analysis by the Method of Moments

Electronics ◽

10.3390/electronics10111316 ◽

2021 ◽

Vol 10 (11) ◽

pp. 1316

Author(s):

Carlos-Ivan Paez-Rueda ◽

Arturo Fajardo ◽

Manuel Pérez ◽

Gabriel Perilla

Keyword(s):

Numerical Integration ◽

Method Of Moments ◽

Computing Time ◽

Basis Functions ◽

Wire Antenna ◽

Complex Geometries ◽

Point Matching ◽

Piecewise Constant ◽

Matching Procedure ◽

Time Required

This paper proposes new closed expressions of self-impedance using the Method of Moments with the Point Matching Procedure and piecewise constant and linear basis functions in different configurations, which allow saving computing time for the solution of wire antennas with complex geometries. The new expressions have complexity O(1) with well-defined theoretical bound errors. They were compared with an adaptive numerical integration. We obtain an accuracy between 7 and 16 digits depending on the chosen basis function and segmentation used. Besides, the computing time involved in the calculation of the self-impedance terms was evaluated and compared with the time required by the adaptative quadrature integration solution of the same problem. Expressions have a run-time bounded between 50 and 200 times faster than an adaptive numerical integration assuming full computation of all constant of the expressions.

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A CO-POLARIZED MICROWAVE ABSORBER WITH DUAL MODE RESONANCE BASED ON DUAL SPLIT RING GEOMETRY FOR WI-MAX AND WLAN APPLICATIONS

Progress In Electromagnetics Research M ◽

10.2528/pierm19080804 ◽

2019 ◽

Vol 86 ◽

pp. 145-152

Author(s):

Gobinda Sen ◽

Anumoy Ghosh ◽

Mukesh Kumar ◽

Sk. Nurul Islam ◽

Santanu Das

Keyword(s):

Microwave Absorber ◽

Dual Mode ◽

Split Ring ◽

Ring Geometry

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A Mixed quadrature rule for numerical integration of analytic functions by using fejer and gaussian quadrature rules

Bulletin of Pure & Applied Sciences- Mathematics and Statistics ◽

10.5958/2320-3226.2015.00005.3 ◽

2015 ◽

Vol 34e (1and2) ◽

pp. 61

Author(s):

Dwiti Krushna Behera ◽

Rajani Ballav Dash

Keyword(s):

Numerical Integration ◽

Analytic Functions ◽

Gaussian Quadrature ◽

Quadrature Rule ◽

Quadrature Rules

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Midpoint Derivative-Based Closed Newton-Cotes Quadrature

Abstract and Applied Analysis ◽

10.1155/2013/492507 ◽

2013 ◽

Vol 2013 ◽

pp. 1-10 ◽

Cited By ~ 5

Author(s):

Weijing Zhao ◽

Hongxing Li

Keyword(s):

Numerical Integration ◽

Computational Cost ◽

Point Of View ◽

Quadrature Rules ◽

Numerical Examples ◽

Error Terms

A novel family of numerical integration of closed Newton-Cotes quadrature rules is presented which uses the derivative value at the midpoint. It is proved that these kinds of quadrature rules obtain an increase of two orders of precision over the classical closed Newton-Cotes formula, and the error terms are given. The computational cost for these methods is analyzed from the numerical point of view, and it has shown that the proposed formulas are superior computationally to the same order closed Newton-Cotes formula when they reduce the error below the same level. Finally, some numerical examples show the numerical superiority of the proposed approach with respect to closed Newton-Cotes formulas.

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Closed Newton-Cotes Trigonometrically-Fitted Formulae for Numerical Integration of the Schrödinger Equation

Computing Letters ◽

10.1163/157404007779994269 ◽

2007 ◽

Vol 3 (1) ◽

pp. 45-57 ◽

Cited By ~ 47

Author(s):

T.E. Simos

Keyword(s):

Numerical Integration ◽

Symplectic Geometry ◽

Efficient Solution ◽

Symplectic Integrators ◽

Multilayer Structures ◽

Symplectic Methods ◽

One Dimensional ◽

One Step ◽

Differential Methods ◽

Symplectic Schemes

In this paper we investigate the connection between closed Newton-Cotes formulae, trigonometrically-fitted differential methods, symplectic integrators and efficient solution of the Schr¨odinger equation. Several one step symplectic integrators have been produced based on symplectic geometry, as one can see from the literature. However, the study of multistep symplectic integrators is very poor. Zhu et. al. [1] has studied the symplectic integrators and the well known open Newton-Cotes differential methods and as a result has presented the open Newton-Cotes differential methods as multilayer symplectic integrators. The construction of multistep symplectic integrators based on the open Newton-Cotes integration methods was investigated by Chiou and Wu [2]. In this paper we investigate the closed Newton-Cotes formulae and we write them as symplectic multilayer structures. We also develop trigonometrically-fitted symplectic methods which are based on the closed Newton-Cotes formulae. We apply the symplectic schemes to the well known one-dimensional Schr¨odinger equation in order to investigate the efficiency of the proposed method to these type of problems.

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