Vector field approximation using radial basis functions

The paper deals with a div-curl approximation problem by weighted minimizing splines. The weighted minimizing splines are an extension of the well-known thin plate splines and are radial basis functions which allow the approximation or the interpolation of a scalar function from given scattered data. In this paper, we show that the theory of the weighted minimizing splines may also be used for the approximation or for the interpolation of a vector field controlled by the divergence and the curl of the vector field. Numerical examples are given to show the efficiency of this method.

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A New Approach to Vector Field Interpolation, Classification and Robust Critical Points Detection Using Radial Basis Functions

Advances in Intelligent Systems and Computing - Cybernetics and Algorithms in Intelligent Systems ◽

10.1007/978-3-319-91192-2_12 ◽

2018 ◽

pp. 109-115 ◽

Cited By ~ 1

Author(s):

Vaclav Skala ◽

Michal Smolik

Keyword(s):

Vector Field ◽

Radial Basis Functions ◽

Critical Points ◽

Basis Functions ◽

New Approach ◽

Radial Basis

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A Sequential Optimization Approach for Honeycomb Crashworthiness using Radial Basis Functions

10.26678/abcm.mecsol2019.msl19-0027 ◽

2019 ◽

Author(s):

Matheus Rodrigues ◽

Marco Antonio Luersen

Keyword(s):

Radial Basis Functions ◽

Basis Functions ◽

Sequential Optimization ◽

Optimization Approach ◽

Radial Basis

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Meshless Euler solver using radial basis functions for solving inviscid compressible flows

10.31274/rtd-180813-11008 ◽

2006 ◽

Author(s):

Prasad Venkateshwara Tota

Keyword(s):

Radial Basis Functions ◽

Compressible Flows ◽

Basis Functions ◽

Radial Basis ◽

Euler Solver ◽

Inviscid Compressible Flows

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Local learning by sparse radial basis functions

9th International Conference on Artificial Neural Networks: ICANN '99 ◽

10.1049/cp:19991114 ◽

1999 ◽

Author(s):

Y. Grandvalet

Keyword(s):

Radial Basis Functions ◽

Basis Functions ◽

Local Learning ◽

Radial Basis

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Application of the meshless local Petrov-Galerkin method with radial basis functions to electromagnetic modelling

Fifth IEE International Conference on Computation in Electromagnetics - CEM 2004 ◽

10.1049/cp:20040422 ◽

2004 ◽

Author(s):

S.A. Viana

Keyword(s):

Galerkin Method ◽

Radial Basis Functions ◽

Basis Functions ◽

Electromagnetic Modelling ◽

Radial Basis

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Spectrum cartography using adaptive radial basis functions: Experimental validation

2017 IEEE 18th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC) ◽

10.1109/spawc.2017.8227752 ◽

2017 ◽

Author(s):

Henning Idsoe ◽

Mohamed Hamid ◽

Thomas Jordbru ◽

Linga Reddy Cenkeramaddi ◽

Baltasar Beferull-Lozano

Keyword(s):

Radial Basis Functions ◽

Experimental Validation ◽

Basis Functions ◽

Radial Basis

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A meshless Galerkin scheme for the approximate solution of nonlinear logarithmic boundary integral equations utilizing radial basis functions

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2017.11.020 ◽

2018 ◽

Vol 333 ◽

pp. 362-381 ◽

Cited By ~ 14

Author(s):

Pouria Assari ◽

Mehdi Dehghan

Keyword(s):

Approximate Solution ◽

Integral Equations ◽

Radial Basis Functions ◽

Boundary Integral Equations ◽

Boundary Integral ◽

Basis Functions ◽

Galerkin Scheme ◽

Radial Basis

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Interpolation using Gaussian radial basis functions with optimized shape parameter applied in vertical deformation analysis

Geodesy and Geodynamics ◽

10.1016/j.geog.2021.02.004 ◽

2021 ◽

Author(s):

M.A. Khalili ◽

B. Voosoghi

Keyword(s):

Radial Basis Functions ◽

Shape Parameter ◽

Basis Functions ◽

Deformation Analysis ◽

Vertical Deformation ◽

Radial Basis

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Biharmonic navigation using radial basis functions

Robotica ◽

10.1017/s0263574721000709 ◽

2021 ◽

pp. 1-12

Author(s):

Xu-Qian Fan ◽

Wenyong Gong

Keyword(s):

Finite Difference ◽

Boundary Conditions ◽

Radial Basis Functions ◽

Real World ◽

Biharmonic Equation ◽

Finite Difference Methods ◽

Basis Functions ◽

Large Size ◽

Radial Basis ◽

Difference Methods

Abstract Path planning has been widely investigated by many researchers and engineers for its extensive applications in the real world. In this paper, a biharmonic radial basis potential function (BRBPF) representation is proposed to construct navigation fields in 2D maps with obstacles, and it therefore can guide and design a path joining given start and goal positions with obstacle avoidance. We construct BRBPF by solving a biharmonic equation associated with distance-related boundary conditions using radial basis functions (RBFs). In this way, invalid gradients calculated by finite difference methods in large size grids can be preventable. Furthermore, paths constructed by BRBPF are smoother than paths constructed by harmonic potential functions and other methods, and plenty of experimental results demonstrate that the proposed method is valid and effective.

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