On the Dimension of Bivariate C1 Cubic Spline Space with Homogeneous Boundary Conditions over a CT Triangulation

2011 ◽  
Vol 50-51 ◽  
pp. 488-492
Author(s):  
Dian Xuan Gong ◽  
Feng Gong Lang
Keyword(s):  
Boundary Conditions ◽  
Computer Aided Design ◽  
Numerical Approximation ◽  
Cubic Spline ◽  
Spline Space ◽  
Singular Boundary ◽  
Piecewise Polynomial ◽  
Nite Element ◽  
Bivariate Spline ◽  
Aided Design

A bivariate spline is a piecewise polynomial with some smoothness de ned on a parti- tion. In this paper, we mainly study the dimensions of bivariate C1 cubic spline spaces S1;0 3 (CT ) and S1;1 3 (CT ) with homogeneous boundary conditions over CT by using interpolating technique, where CT stands for a CT triangulation. The dimensions are related with the numbers of the inter vertices and the singular boundary vertices. The results of this paper can be applied in many elds such as the nite element method for partial di erential equation, computer aided design, numerical approximation, and so on.

scholarly journals W-Band Characterization of Grounded Frequency Selective Surface Arrays Composed of Nonequal Slot Length Subarrays

2009 ◽  
Vol 2009 ◽  
pp. 1-7 ◽  
Author(s):  
S. Islam ◽  
J. Stiens ◽  
G. Poesen ◽  
I. Jaeger ◽  
W. De Raedt ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Computer Aided Design ◽  
Experimental Approach ◽  
Frequency Selective Surface ◽  
Slot Length ◽  
W Band ◽  
Cad Simulation ◽  
Frequency Selective ◽  
The Difference ◽  
Aided Design

We present the design and construction of Frequency Selective Surface arrays composed of two subarrays of different slot lengths. We investigated their response variations with the variation of slot length differences of the elementary sub-arrays. Such nonhomogeneous arrays cannot be simulated with Computer Aided Design (CAD) programs because the boundary conditions are not fulfilled by the simulator. In infinite array simulation, the periodic boundary conditions are prescribed on the walls of the unit cell, whereas in the case of sub-arrays of unequal slot length such boundary conditions are not applicable. The CAD simulation of such combined array gives incorrect values of amplitude and phase responses. In this work, we investigate the characteristics of such complex arrays by using heuristic experimental approach. The results of the experimental approach demonstrate that the resultant reflection amplitude and phase of such complex array depend on the difference of slot lengths (ΔL) of the two sub-arrays.

scholarly journals CFD-CAA Method for Prediction of Pseudosound and Emitted Noise in Quadcopter Propeller

2022 ◽  
pp. 21-25
Author(s):  
Sergey Timushev ◽  
Alexey Yakovlev ◽  
Dmitry Klimenko
Keyword(s):  
Boundary Conditions ◽  
Acoustic Impedance ◽  
Computer Aided Design ◽  
Aerodynamic Noise ◽  
Compressible Medium ◽  
Computational Domain ◽  
Pressure Pulsations ◽  
Noise Characteristics ◽  
Computer Aided ◽  
Aided Design

Subsonic flow air blade machines like UAV propellers generate intensive noise thus the prediction of acoustic impact, optimization of these machines in order to reduce the level of emitted noise is an urgent engineering task. Currently, the development of calculation methods for determining the amplitudes of pressure pulsations and noise characteristics by CFD-CAA methods is a necessary requirement for the development of computer-aided design methods for blade machines, where the determining factors are the accuracy and speed of calculations. The main objective is to provide industrial computer-aided design systems with a highly efficient domestic software to create optimal designs of UAV blade machines that provide a given level of pressure pulsations in the flow part and radiated noise. It comprises: 1) creation of a method for the numerical simulation of sound generation using the correct decomposition of the initial equations of hydrodynamics of a compressible medium and the selection of the source of sound waves in a three-dimensional definition, taking into account the rotation of blades and their interaction with the stator part of the UAV; 2) decomposition of the boundary conditions accounting pseudo-sound disturbances and the complex acoustic impedance at the boundaries of the computational domain 3) development of an effective SLAE solver for solving the acoustic-vortex equation in complex arithmetic (taking into account the boundary conditions in the form of complex acoustic impedance); 4) testing of a new method at all stages of development using experimental data on the generation of pressure pulsations and aerodynamic noise, including a propeller noise measurements.

scholarly journals DETERMINATION OF BOUNDARY CONDITIONS FOR THE RADIATION PATTERN OF A MICROELECTRO-OPTICAL INTELLIGENT PASSIVE INFRARED MOTION DETECTOR

2021 ◽  
Vol 3 (1) ◽  
pp. 31-36
Author(s):  
Ruslan Holovatskyy ◽  
◽  
Mykhaylo Lobur ◽  
Keyword(s):  
Boundary Conditions ◽  
Computer Aided Design ◽  
Block Diagram ◽  
Primary Sources ◽  
Motion Detector ◽  
New Developments ◽  
Aided Design ◽  
Motion Detectors ◽  
Passive Infrared

In this paper, a block diagram of a microelectro-optical intelligent passive infrared motion detector is proposed. On the basis of the proposed structural scheme and analytically conducted synthetic processing of information from primary sources [5-17], boundary conditions for the directivity diagram of such a detector are determined. The analytical information collected in this article will be necessary for further modeling in computer-aided design with a view to new developments and improvements to existing motion detectors.

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