scholarly journals Method of Moments Based on Equivalent Periodic Problem and FFT with NURBS Surfaces for Analysis of Multilayer Periodic Structures

Electronics ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 234 ◽  
Author(s):  
Rafael Florencio ◽  
Álvaro Somolinos ◽  
Iván González ◽  
Felipe Cátedra
Keyword(s):  
Method Of Moments ◽  
Original Problem ◽  
Periodic Structures ◽  
Periodic Problem ◽  
Nurbs Surface ◽  
Direct Computation ◽  
Cpu Time ◽  
Phase Errors ◽  
Nurbs Surfaces ◽  
Time Savings

In this paper, an efficient technique of computation of method of moments (MM) matrix entries for multilayer periodic structures with NURBS surface and Bézier patches modelling is proposed. An approximation in terms of constant pulses of generalized rooftop basis functions (BFs) defined on Bézier patches is proposed. This approximation leads discrete convolutions instead of usual continuous convolution between Green’s functions and BFs obtained by the direct mixed potential integral equation (MPIE) approach. An equivalent periodic problem (EPP) which contains the original problem is proposed to transform the discrete convolutions in discrete cyclic convolutions. The resultant discrete cyclic convolutions are computed by efficiently using the Fast Fourier Transform (FFT) procedure. The performance of the proposed method and direct computation of the MM entries are compared for phases of reflection coefficient. The proposed method is between 9 and 50 times faster than the direct computation for phase errors less than 1 deg. The proposed method exhibits a behaviour of CPU time consumption of O(NbLog10Nb) as the number Nb of BFs increases. This behaviour provides significant CPU time savings with respect to the expected behaviour of O(Nb2) provided by the direct computation of the MM matrix entries.

scholarly journals BICGSTAB-FFT Method of Moments with NURBS for Analysis of Planar Generic Layouts Embedded in Large Multilayer Structures

Electronics ◽  
2020 ◽  
Vol 9 (9) ◽  
pp. 1476 ◽  
Author(s):  
Rafael Florencio ◽  
Álvaro Somolinos ◽  
Iván González ◽  
Felipe Cátedra
Keyword(s):  
Method Of Moments ◽  
Multilayer Structure ◽  
Fourier Transforms ◽  
Periodic Problem ◽  
Basis Functions ◽  
Multilayer Structures ◽  
Method Of Moment ◽  
Efficient Computation ◽  
Normalized Error ◽  
Nurbs Surfaces

BICGSTAB-FFT method of moment (MM) scheme is proposed to analyze several levels of planar generic layouts embedded in large multilayer structures when the layout geometries are modeled by NURBS surfaces. In this scheme, efficient computation of normalized error defined in iterative bi-conjugate gradient stabilized (BICGSTAB) method for large multilayer structure analysis problems is implemented. The efficient computation is based on pulse expansion with dense equi-spaced mesh of generalized rooftop basis functions (BFs) defined on NURBS surfaces and equivalent periodic problem (EPP) in order to apply fast Fourier transforms (FFT). Moreover, efficient computation of Green’s functions for multilayer structure is implemented for near and far field regions. Experimental and numerical validations of whole printed reflect array antennas of electrical size between 8 and 16 times the vacuum wavelengths are shown. In these validations, CPU time consumptions of the proposed method are obtained with results between few minutes and half an hour using a conventional laptop.

Method of Moments (MoM) for the Analysis of Dielectric Double Periodic Structures

2012 ◽  
Vol 241-244 ◽  
pp. 1531-1534
Author(s):  
Shan Zhao ◽  
Nai Qian Zhang ◽  
Dong Li
Keyword(s):  
Method Of Moments ◽  
Periodic Boundary ◽  
Periodic Structures ◽  
Periodic Boundary Conditions ◽  
Spatial Domain ◽  
Three Dimension ◽  
Volume Integral ◽  
Volume Integral Equation ◽  
Filling Time ◽  
Lossy Material

The space-domain volume integral equation (VIE) method is presented for the analysis of three-dimension (3-D) scattering from dielectric frequency selective structures (DFSS) involved homogeneous and inhomogeneous lossy material. The method solves directly for the electric field in order to easily enable periodic boundary conditions in the spatial domain. The computation of the spatial domain periodic Green’s function (PGF) is accelerated by the modified Ewald transformation. Optimized interpolation procedures for the PGFs can be applied, resulting in a considerable reduction of matrix-filling time without any significant effect on the accuracy.

The Dynamics of a Deformable Body Experiencing Large Displacements

1988 ◽  
Vol 55 (3) ◽  
pp. 676-680 ◽  
Author(s):  
W. P. Koppens ◽  
A. A. H. J. Sauren ◽  
F. E. Veldpaus ◽  
D. H. van Campen
Keyword(s):  
Rigid Body ◽  
Mass Matrix ◽  
Deformable Body ◽  
Equations Of Motion ◽  
Body Motion ◽  
General Description ◽  
Large Displacements ◽  
Displacement Fields ◽  
Cpu Time ◽  
Time Savings

A general description of the dynamics of a deformable body experiencing large displacements is presented. These displacements are resolved into displacements due to deformation and displacements due to rigid body motion. The former are approximated with a linear combination of assumed displacement fields. D’Alembert’s principle is used to derive the equations of motion. For this purpose, the rigid body displacements and the displacements due to deformation have to be independent. Commonly employed conditions for achieving this are reviewed. It is shown that some conditions lead to considerably simpler equations of motion and a sparser mass matrix, resulting in CPU time savings when used in a multibody program. This is illustrated with a uniform beam and a crank-slider mechanism.

scholarly journals An Improvement on the Upper Bounds of the Partial Derivatives of NURBS Surfaces

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1382
Author(s):  
Ye Tian ◽  
Tao Ning ◽  
Jixing Li ◽  
Jianmin Zheng ◽  
Zhitong Chen
Keyword(s):  
Upper Bounds ◽  
Basis Functions ◽  
Nurbs Surface ◽  
Degree Reduction ◽  
B Spline ◽  
Partial Derivatives ◽  
Spline Basis ◽  
Rational Bézier Surface ◽  
Nurbs Surfaces ◽  
Derivatives Of

The Non-Uniform Rational B-spline (NURBS) surface not only has the characteristics of the rational Bézier surface, but also has changeable knot vectors and weights, which can express the quadric surface accurately. In this paper, we investigated new bounds of the first- and second-order partial derivatives of NURBS surfaces. A pilot study was performed using inequality theorems and degree reduction of B-spline basis functions. Theoretical analysis provides simple forms of the new bounds. Numerical examples are performed to illustrate that our method has sharper bounds than the existing ones.

Sampling for Free Form Surfaces Inspection Planning

1999 ◽  
Author(s):  
Diaa F. ElKott ◽  
Hoda A. ElMaraghy ◽  
Ashraf O. Nassef
Keyword(s):  
Gaussian Curvature ◽  
Patch Size ◽  
Free Form ◽  
Maximum Deviation ◽  
Inspection Planning ◽  
Nurbs Surface ◽  
Cpu Time ◽  
Inspection Process ◽  
Data Points ◽  
Free Form Surfaces

Abstract This paper presents four methodologies for sampling of free form surfaces and discusses their merits and application. These are equi-parametric sampling, patch size based sampling, patch mean Gaussian curvature based sampling, and the combined patch size and patch mean Gaussian curvature based sampling. The locations of points inspected for a NURBS surface are optimized to minimize the maximum deviation between the surface fitted to the data points and the designed surface. During optimization, the inspection process is simulated, a parametric NURBS surface is fitted to the data points and the maximum deviation between the fitted and designed surfaces is minimized. Algorithms for the application of the sampling methodologies were implemented using MATLAB software. Each sampling methodology is explained, and illustrated by an example. The performance of the different sampling methodologies are compared in terms of the maximum deviation obtained and the CPU time needed to accomplish the sampling task.

Acceleration of Wavelet-based Method of Moments for Periodic Structures

2009 ◽  
Vol 129 (10) ◽  
pp. 729-735
Author(s):  
Hidetoshi Chiba ◽  
Kazushi Nishizawa ◽  
Hiroaki Miyashita ◽  
Yoshihiko Konishi
Keyword(s):  
Method Of Moments ◽  
Periodic Structures

Geometric Modeling of Compound NURBS Surfaces

2020 ◽  
Vol 38 (2A) ◽  
pp. 277-287
Author(s):  
Ali K. Alwan ◽  
Wisam K. Hamdan
Keyword(s):  
Geometric Modeling ◽  
Design Method ◽  
Control Points ◽  
Sculptured Surfaces ◽  
Nurbs Surface ◽  
Surface Design ◽  
Spline Basis ◽  
Automotive Parts ◽  
Nurbs Surfaces ◽  
Complex Features

The design of sculptured surfaces occupies an essential area in the field of modern industrial, aerospace, and medical applications. The challenge is to design products that have complex features efficiently with great flexibility of editing in certain regions without affecting other regions, which the designer has no intent to modify. In this paper, we propose a surface design method based on compound NURBS surface to model automotive parts with 400 control points. First, a Non-Uniform B-Spline basis function is derived with a cubic degree and 20 control points. This method is utilized to design car posterior door, car hood, and rear car door as case studies.

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.

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