Geometrical representation infinitely smooth curves and surfaces for higher order computational electromagnetics

2011 ◽  
Author(s):  
F. Vico-Bondia ◽  
M. F. Bataller ◽  
D. S. Escuderos ◽  
E. A. Alos
Keyword(s):  
Computational Electromagnetics ◽  
Higher Order ◽  
Smooth Curves ◽  
Geometrical Representation ◽  
Curves And Surfaces

scholarly journals A Family of Integer-Point Ternary Parametric Subdivision Schemes

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Ghulam Mustafa ◽  
Muhammad Asghar ◽  
Shafqat Ali ◽  
Ayesha Afzal ◽  
Jia-Bao Liu
Keyword(s):  
General Formula ◽  
Integer Point ◽  
Laurent Polynomial ◽  
Polynomial Method ◽  
Subdivision Schemes ◽  
Smooth Curves ◽  
Curves And Surfaces

New subdivision schemes are always required for the generation of smooth curves and surfaces. The purpose of this paper is to present a general formula for family of parametric ternary subdivision schemes based on the Laurent polynomial method. The different complexity subdivision schemes are obtained by substituting the different values of the parameter. The important properties of the proposed family of subdivision schemes are also presented. The continuity of the proposed family is C 2 m . Comparison shows that the proposed family of subdivision schemes has higher degree of polynomial generation, degree of polynomial reproduction, and continuity compared with the exiting subdivision schemes. Maple software is used for mathematical calculations and plotting of graphs.

scholarly journals Efficient and Accurate Computational Electromagnetics Approach to Precipitation Particle Scattering Analysis Based on Higher-Order Method of Moments Integral Equation Modeling

2015 ◽  
Vol 32 (10) ◽  
pp. 1745-1758 ◽  
Author(s):  
E. Chobanyan ◽  
N. J. Šekeljić ◽  
A. B. Manić ◽  
M. M. Ilić ◽  
V. N. Bringi ◽  
...  
Keyword(s):  
Integral Equation ◽  
Method Of Moments ◽  
Matrix Method ◽  
Computational Electromagnetics ◽  
Higher Order ◽  
Equation Modeling ◽  
Particle Scattering ◽  
Order Method ◽  
Higher Order Method ◽  
Dda Method

AbstractA new full-wave computational electromagnetics (CEM) approach to precipitation particle scattering analysis based primarily on a higher-order method of moments (MoM) for solving surface integral equations (SIEs) is proposed, as an alternative and addition to the conventionally used tools in this area. This is a well-established CEM approach that has not been applied, evaluated, discussed, or compared with other approaches in the scattering analysis of precipitation particles so far. Several characteristic examples of scattering from precipitation particles of various shapes demonstrate the capabilities and potential of the presented numerical methodology, and discuss its advantages over both discrete dipole approximation (DDA) and -matrix methods in cases considered. In particular, it is shown that the higher-order MoM-SIE approach is much faster, more accurate, and more robust than the DDA method, and much more general and versatile than the -matrix method. In addition, the paper illustrates problems with the convergence of the DDA method in some cases with high-contrast dielectric materials and large electrical sizes of particles and with the convergence of the -matrix method in some cases with electrically large or geometrically complex (viz., with a large aspect ratio) particles. For simulations of continuously inhomogeneous scatterers (e.g., melting ice particles), a higher-order MoM volume integral equation (VIE) technique is used, as the study’s secondary methodology. The results also indicate the necessity for numerically rigorous and computationally efficient realistic precipitation particle modeling in weather scattering applications, which is becoming even more important as the sensor frequencies of radar/radiometric systems are increasing.

scholarly journals A MATRIX PRESENTATION OF HIGHER ORDER DERIVATIVES OF BÉZIER CURVE AND SURFACE

2021 ◽  
Vol 21 (1) ◽  
pp. 77-90
Author(s):  
TUBA AĞIRMAN AYDIN
Keyword(s):  
Higher Order ◽  
Control Points ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Algebraic Form ◽  
Important Place ◽  
Curves And Surfaces ◽  
The Matrix ◽  
Special Matrix ◽  
Derivatives Of

In this study, the Bézier curves and surfaces, which have an important place in interactive design applications, are expressed in matrix form using a special matrix that gives the coefficients of the Bernstein base polynomial. The matrix forms of higher order derivatives of the Bézier curves and surfaces are obtained. It is demonstrated by numerical examples that the bidirectional transition between the control points and parametric equations of the Bézier curves and surfaces can be easily achieved using these matrix forms. In addition, it is demonstrated that this type of curve and surface, whose control points are known, its higher order derivatives can be calculated without it's parametric equations. In this study, the Bézier curves and surfaces are presented in a more easily understandable and easy to use format in algebraic form for designers.

Higher order interpolatory vector bases for computational electromagnetics

1997 ◽  
Vol 45 (3) ◽  
pp. 329-342 ◽  
Author(s):  
R.D. Graglia ◽  
D.R. Wilton ◽  
A.F. Peterson
Keyword(s):  
Computational Electromagnetics ◽  
Higher Order
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