scholarly journals Numerical quadrature over smooth, closed surfaces

2016 ◽  
Vol 472 (2194) ◽  
pp. 20160401 ◽  
Author(s):  
J. A. Reeger ◽  
B. Fornberg ◽  
M. L. Watts
Keyword(s):  
Computational Complexity ◽  
Efficient Method ◽  
Basis Function ◽  
Numerical Approximation ◽  
One Dimension ◽  
Radial Basis Function Interpolation ◽  
Definite Integrals ◽  
Closed Surfaces ◽  
Appl Math ◽  
Subsequent Integration

The numerical approximation of definite integrals, or quadrature, often involves the construction of an interpolant of the integrand and its subsequent integration. In the case of one dimension it is natural to rely on polynomial interpolants. However, their extension to two or more dimensions can be costly and unstable. An efficient method for computing surface integrals on the sphere is detailed in the literature (Reeger & Fornberg 2016 Stud. Appl. Math. 137 , 174–188. ( doi:10.1111/sapm.12106 )). The method uses local radial basis function interpolation to reduce computational complexity when generating quadrature weights for any given node set. This article generalizes this method to arbitrary smooth closed surfaces.

Impulse Noise Removal Using Adaptive Radial Basis Function Interpolation

2016 ◽  
Vol 36 (3) ◽  
pp. 1192-1223 ◽  
Author(s):  
T. Veerakumar ◽  
Ravi Prasad K. Jagannath ◽  
Badri Narayan Subudhi ◽  
S. Esakkirajan
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Impulse Noise ◽  
Noise Removal ◽  
Radial Basis Function Interpolation ◽  
Impulse Noise Removal ◽  
Radial Basis

scholarly journals Solution of the quantum fluid dynamical equations with radial basis function interpolation

2000 ◽  
Vol 61 (5) ◽  
pp. 5967-5976 ◽  
Author(s):  
Xu-Guang Hu ◽  
Tak-San Ho ◽  
Herschel Rabitz ◽  
Attila Askar
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Dynamical Equations ◽  
Quantum Fluid ◽  
Radial Basis Function Interpolation ◽  
Radial Basis

Solving Mid-Frequency Acoustic Problem by the Meshless Method

2013 ◽  
Vol 444-445 ◽  
pp. 1471-1476
Author(s):  
Shuang Wang ◽  
Qi Bai Huang ◽  
Shan De Li
Keyword(s):  
Boundary Condition ◽  
Finite Element ◽  
Radial Basis Function ◽  
Efficient Method ◽  
Basis Function ◽  
Meshless Method ◽  
Medium Frequency ◽  
Pollution Effect ◽  
Acoustic Problem ◽  
Engineering Problems

It is well known that traditional finite element (FEM) is an efficient method in solving engineering problems. However, when solving the acoustic problems in medium frequency, FEM suffers from the so-called pollution effect, which is directly related to the dispersion. In this paper, meshless method based on radial basis function (RBF) is introduced to solve the acoustic problem, which shows that the dispersion can be greatly reduced, thus it is very suitable for the solution of mid-frequency acoustic problem. In addition, an algorithm is presented to treat the boundary condition, which improves the performance of the meshless method.

scholarly journals Rapid Interactive and Intuitive Segmentation of 3D Medical Images Using Radial Basis Function Interpolation

2017 ◽  
Vol 3 (4) ◽  
pp. 56
Author(s):  
Tanja Kurzendorfer ◽  
Peter Fischer ◽  
Negar Mirshahzadeh ◽  
Thomas Pohl ◽  
Alexander Brost ◽  
...  
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Medical Images ◽  
Radial Basis Function Interpolation ◽  
Radial Basis

scholarly journals A Frame-Based Conjugate Gradients Direct Search Method with Radial Basis Function Interpolation Model

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Xiaowei Fang ◽  
Qin Ni
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Direct Search ◽  
Search Method ◽  
Conjugate Gradients ◽  
Test Problems ◽  
Interpolation Model ◽  
Direct Search Method ◽  
Radial Basis Function Interpolation ◽  
Radial Basis

In this paper, we propose a new hybrid direct search method where a frame-based PRP conjugate gradients direct search algorithm is combined with radial basis function interpolation model. In addition, the rotational minimal positive basis is used to reduce the computation work at each iteration. Numerical results for solving the CUTEr test problems show that the proposed method is promising.

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