Quadrature rules for numerical integration over triangles and tetrahedra

1996 ◽  
Vol 38 (3) ◽  
pp. 100-102 ◽  
Author(s):  
J.S. Savage ◽  
A.F. Peterson
Keyword(s):  
Numerical Integration ◽  
Quadrature Rules

scholarly journals Midpoint Derivative-Based Closed Newton-Cotes Quadrature

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
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.

scholarly journals Efficient Quadrature Rules for Numerical Integration Based on Linear Legendre Multi-Wavelets

2019 ◽  
Vol 1366 ◽  
pp. 012092
Author(s):  
Nur Neesha Alimin ◽  
Ahmad Fadly Nurullah Rasedee ◽  
Mohammad Hasan Abdul Sathar ◽  
Anvarjon A. Ahmedov ◽  
Muhammad Asyraf Asbullah
Keyword(s):  
Numerical Integration ◽  
Quadrature Rules

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

Electronics ◽  
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.

Two Sharp Perturbed Midpoint Inequalities

2014 ◽  
Vol 472 ◽  
pp. 527-531
Author(s):  
Yan Xia Shi ◽  
Yu Min Tao ◽  
Yu Pan
Keyword(s):  
Numerical Integration ◽  
Error Bounds ◽  
Kernel Functions ◽  
Quadrature Rules

In this study, two new sharp perturbed midpoint inequalities are proved by establishing proper kernel functions. These results enlarge applicability of the corresponding quadrature rules with respect to the obtained error bounds. Applications in numerical integration are also given.

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