The Application of Barycentric Subdivision Method for Numerical Integration in Method of Moments

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

Electronics ◽

10.3390/electronics9122043 ◽

2020 ◽

Vol 9 (12) ◽

pp. 2043

Author(s):

Rafael Florencio ◽

Álvaro Somolinos ◽

Iván González ◽

Felipe Cátedra ◽

Lorena Lozano

Keyword(s):

Numerical Integration ◽

Method Of Moments ◽

Quadrature Rules ◽

Multilayer Structures ◽

Previous Approach ◽

Split Ring ◽

Time Consumption ◽

Cpu Time ◽

Ring Geometry ◽

Specific Analysis

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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Simulating Univariate and Multivariate Tukey g-and-h Distributions Based on the Method of Percentiles

ISRN Probability and Statistics ◽

10.1155/2014/645823 ◽

2014 ◽

Vol 2014 ◽

pp. 1-10 ◽

Cited By ~ 4

Author(s):

Tzu Chun Kuo ◽

Todd C. Headrick

Keyword(s):

Closed Form ◽

Numerical Integration ◽

Method Of Moments ◽

Data Generation ◽

Shape Parameters ◽

Distribution Fitting ◽

Closed Form Solutions ◽

Nonnormal Distributions ◽

Simulation Results ◽

Family Of Distributions

This paper derives closed-form solutions for the g-and-h shape parameters associated with the Tukey family of distributions based on the method of percentiles (MOP). A proposed MOP univariate procedure is described and compared with the method of moments (MOM) in the context of distribution fitting and estimating skew and kurtosis functions. The MOP methodology is also extended from univariate to multivariate data generation. A procedure is described for simulating nonnormal distributions with specified Spearman correlations. The MOP procedure has an advantage over the MOM because it does not require numerical integration to compute intermediate correlations. Simulation results demonstrate that the proposed MOP procedure is superior to the MOM in terms of distribution fitting, estimation, relative bias, and relative error.

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The orbit of Pluto over a long interval of time

Symposium - International Astronomical Union ◽

10.1017/s0074180900105509 ◽

1966 ◽

Vol 25 ◽

pp. 227-229 ◽

Cited By ~ 1

Author(s):

D. Brouwer

Keyword(s):

Periodic Orbit ◽

Numerical Integration ◽

Restricted Problem ◽

Three Dimensional ◽

The Third ◽

Circular Restricted Problem ◽

Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

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