A two-stage adaptive scheme based on RBF collocation for solving elliptic PDEs
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Publication:2192500
DOI10.1016/j.camwa.2020.01.018zbMath1469.65168OpenAlexW3003924083WikidataQ114201569 ScholiaQ114201569MaRDI QIDQ2192500
Roberto Cavoretto, Alessandra De Rossi
Publication date: 17 August 2020
Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.camwa.2020.01.018
radial basis functionscollocation methodsadaptive algorithmspartial differential equationsmeshfree approximation
Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Algorithms for approximation of functions (65D15) Numerical radial basis function approximation (65D12)
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Uses Software
Cites Work
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- Recent advances on radial basis function collocation methods
- Adaptive meshless centres and RBF stencils for Poisson equation
- On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals
- A collection of 2D elliptic problems for testing adaptive grid refinement algorithms
- On convergent numerical algorithms for unsymmetric collocation
- Smoothing noisy data with spline functions: Estimating the correct degree of smoothing by the method of generalized cross-validation
- Improved multiquadric method for elliptic partial differential equations via PDE collocation on the boundary
- Implicit local radial basis function interpolations based on function values
- \textsc{OpenCL} based parallel algorithm for RBF-PUM interpolation
- Adaptive meshless refinement schemes for RBF-PUM collocation
- Adaptive RBF-FD method for elliptic problems with point singularities in 2D
- On optimization of the RBF shape parameter in a grid-free local scheme for convection dominated problems over non-uniform centers
- Multiquadrics -- a scattered data approximation scheme with applications to computational fluid-dynamics. II: Solutions to parabolic, hyperbolic and elliptic partial differential equations
- On unsymmetric collocation by radial basis functions
- An algorithm for selecting a good value for the parameter \(c\) in radial basis function interpolation
- On the selection of a good value of shape parameter in solving time-dependent partial differential equations using RBF approximation method
- RBF-based partition of unity methods for elliptic PDEs: adaptivity and stability issues via variably scaled kernels
- Error indicators and refinement strategies for solving Poisson problems through a RBF partition of unity collocation scheme
- Efficient implementation of adaptive P1-FEM in Matlab
- On choosing ``optimal shape parameters for RBF approximation
- Adaptive residual subsampling methods for radial basis function interpolation and collocation problems
- On the new variable shape parameter strategies for radial basis functions
- RBF Multiscale Collocation for Second Order Elliptic Boundary Value Problems
- Stable Computation of Differentiation Matrices and Scattered Node Stencils Based on Gaussian Radial Basis Functions
- A Fast Adaptive Wavelet Scheme in RBF Collocation for Nearly Singular Potential PDEs
- A Primer on Radial Basis Functions with Applications to the Geosciences
- Generalized Cross-Validation as a Method for Choosing a Good Ridge Parameter
- Radial Basis Functions
- A Least Squares Radial Basis Function Partition of Unity Method for Solving PDEs
- Convergence of Unsymmetric Kernel‐Based Meshless Collocation Methods
- Scattered Data Approximation
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