Journal Article10.1016/j.matcom.2022.02.024
Local radial basis function-finite difference based algorithms for singularly perturbed Burgers' model
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TL;DR: In this article , two mesh-free algorithms based on local radial basis function-finite difference approximation were developed for singularly perturbed Burgers' model by developing two meshfree algorithms.
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About: This article is published in Mathematics and Computers in Simulation. The article was published on 01 Feb 2022. The article focuses on the topics: Computer science & Discretization.
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Iterative optimization method for determining optimal shape parameter in RBF-FD method
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TL;DR: In this paper , the authors proposed a novel iterative optimization method to determine the best parameter c for the Radial basis function finite difference (RBF-FD) method based on the Double Operator Error (DOE).
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Numerical simulations of two-dimensional incompressible Navier-Stokes equations by the backward substitution projection method
Yuhui Zhang,Timon Rabczuk,Ji Lin,Jun Lu,C.S. Chen +4 more
TL;DR: This study explores the feasibility of the backward substitution projection method for simulating two-dimensional incompressible flows, demonstrating its accuracy, efficiency, and convergence through five numerical examples and comparisons with existing meshless methods.
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References
Multiquadric equations of topography and other irregular surfaces
TL;DR: In this paper, a method of representing irregular surfaces that involves the summation of equations of quadric surfaces having unknown coefficients is described, and procedures are given for solving multiquadric equations of topography that are based on coordinate data.
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Scattered data interpolation: tests of some methods
TL;DR: In this paper, the evaluation of methods for scattered data interpolation and some of the results of the tests when applied to a number of methods are presented. But the evaluation process involves evaluation of the methods in terms of timing, storage, accuracy, visual pleasantness of the surface, and ease of implementation.
An algorithm for selecting a good value for the parameter c in radial basis function interpolation
TL;DR: It is shown, numerically, that the value of the optimal c (the value of c that minimizes the interpolation error) depends on the number and distribution of data points, on the data vector, and on the precision of the computation.
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On choosing “optimal” shape parameters for RBF approximation
TL;DR: Extensions of this approach that can be applied in the setting of iterated approximate moving least squares approximation of function value data and for RBF pseudo-spectral methods for the solution of partial differential equations are discussed.