Numerical Study of Wind Field Adjustment with Radial Basis Functions

2012 ◽  
pp. 371-378
Author(s):  
Rafael Reséndiz ◽  
L. Héctor Juárez ◽  
Pedro González-Casanova ◽  
Daniel A. Cervantes ◽  
Christian Gout
Keyword(s):  
Radial Basis Functions ◽  
Wind Field ◽  
Numerical Study ◽  
Basis Functions ◽  
Radial Basis

scholarly journals Numerical study of meshless radial basis functions in the lid driven cavity problem

2018 ◽  
Author(s):  
Eko Prasetya Budiana ◽  
Indarto Indarto ◽  
Deendarlianto Deendarlianto ◽  
Pranowo Pranowo
Keyword(s):  
Radial Basis Functions ◽  
Numerical Study ◽  
Basis Functions ◽  
Driven Cavity ◽  
Radial Basis

scholarly journals Numerical Study of Fractional Mathieu Differential Equation Using Radial Basis Functions

2020 ◽  
Vol 7 (4) ◽  
pp. 568-576
Author(s):  
Hojjat Ghorbani ◽  
Yaghoub Mahmoudi ◽  
Farhad Dastmalchi Saei
Keyword(s):  
Differential Equation ◽  
Radial Basis Functions ◽  
Fractional Derivatives ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Mathieu Equation ◽  
Basis Functions ◽  
Damping Factor ◽  
Radial Basis ◽  
The Right

In this paper, we introduce a method based on Radial Basis Functions (RBFs) for the numerical approximation of Mathieu differential equation with two fractional derivatives in the Caputo sense. For this, we suggest a numerical integration method for approximating the improper integrals with a singularity point at the right end of the integration domain, which appear in the fractional computations. We study numerically the affects of characteristic parameters and damping factor on the behavior of solution for fractional Mathieu differential equation. Some examples are presented to illustrate applicability and accuracy of the proposed method. The fractional derivatives order and the parameters of the Mathieu equation are changed to study the convergency of the numerical solutions.

Characterization of a two-dimensional static wind field using Radial Basis Functions

SIMULATION ◽  
2018 ◽  
Vol 95 (6) ◽  
pp. 561-567
Author(s):  
Brandon Troub ◽  
Rockwell Garrido ◽  
Carlos Montalvo ◽  
JD Richardson
Keyword(s):  
Regression Model ◽  
Radial Basis Functions ◽  
Basis Function ◽  
Wind Field ◽  
Basis Functions ◽  
Two Dimensional ◽  
Sampled Data ◽  
Radial Basis ◽  
Data Points ◽  
Spatially Varying

Radial Basis Functions are a modern way of creating a regression model of a multivariate function when sampled data points are not uniformly distributed in a perfect grid. Radial Basis Functions are well suited to atmospheric characterization when unmanned aerial vehicles (UAVs) are used to sample the given space. Multiple UAVs reduce the time for the Radial Basis Functions to yield a suitable solution to the measured data while data from all aircraft are aggregated and sent to Radial Basis Functions to fit the data. The research presented here focuses on the requirements for a high correlation value between the sampled data and the actual data. It is found that the number of centers is a large driver of the goodness of fit in the Radial Basis Function routine, much like aliasing is an issue in sampling a sinusoidal function. These centers act like a sampling rate for the spatially varying wind field. If the centers are dense enough to fully capture the spatial frequency of the wind field, the Radial Basis Functions will produce a suitable fit. This also requires the number of data points to be larger than the number of centers. The ratio between the number of centers and number of sampled data points declines as the number of centers increases. The results presented here are revealed using a two-dimensional Fourier series analysis coupled to a spatially varying atmospheric wind model and a Radial Basis Function regression model.

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