An iterative adaptive multiquadric radial basis function method for the detection of local jump discontinuities

DOI10.1016/j.apnum.2008.09.002zbMath1162.65314OpenAlexW2015559847MaRDI QIDQ1021618

Vincent R. Durante, Jae-Hun Jung

Publication date: 8 June 2009

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2008.09.002

zbMATH Keywords

iterative methodGibbs phenomenonadaptive methodjump discontinuitymultiquadric radial basis functionslocal jump detection

Mathematics Subject Classification ID

Algorithms for approximation of functions (65D15)

Related Items (13)

Fast iterative adaptive multi-quadric radial basis function method for edges detection of piecewise functions. I: Uniform mesh ⋮ Hybrid Compact-WENO Finite Difference Scheme with Radial Basis Function Based Shock Detection Method for Hyperbolic Conservation Laws ⋮ Iterative adaptive RBF methods for detection of edges in two-dimensional functions ⋮ Escaping Unknown Discontinuous Regions in Blackbox Optimization ⋮ Jumping with variably scaled discontinuous kernels (VSDKs) ⋮ Radial basis function interpolation on irregular domain through conformal transplantation ⋮ Recovery of high order accuracy in radial basis function approximations of discontinuous problems ⋮ A fault detection method based on partition of unity and kernel approximation ⋮ Set membership approximation of discontinuous nonlinear model predictive control laws ⋮ Edge detection methods based on RBF interpolation ⋮ RBF-FD solution for a financial partial-integro differential equation utilizing the generalized multiquadric function ⋮ Hybrid Compact-WENO Finite Difference Scheme with Conjugate Fourier Shock Detection Algorithm for Hyperbolic Conservation Laws ⋮ A shock-capturing meshless scheme using RBF blended interpolation and moving least squares

Cites Work

• Unnamed Item
• A note on the Gibbs phenomenon with multiquadric radial basis functions
• Efficient implementation of essentially nonoscillatory shock-capturing schemes
• Bounds on multivariate polynomials and exponential error estimates for multiquadric interpolation
• Improved accuracy of multiquadric interpolation using variable shape parameters
• Miscellaneous error bounds for multiquadric and related interpolators
• An efficient numerical scheme for Burger equation
• Solving partial differential equations by collocation using radial basis functions
• Circumventing the ill-conditioning problem with multiquadric radial basis functions: Applications to elliptic partial differential equations
• Multiquadric collocation method with integralformulation for boundary layer problems
• Multiquadrics -- a scattered data approximation scheme with applications to computational fluid-dynamics. II: Solutions to parabolic, hyperbolic and elliptic partial differential equations
• Overlapping domain decomposition method by radial basis functions
• Exact explicit time integration of hyperbolic partial differential equations with mesh-free radial basis functions
• Adaptive residual subsampling methods for radial basis function interpolation and collocation problems
• The Runge phenomenon and spatially variable shape parameters in RBF interpolation
• An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws
• Detection of Edges in Spectral Data II. Nonlinear Enhancement
• Spectral Approximation Orders of Radial Basis Function Interpolation on the Sobolev Space
• Spectral convergence of multiquadric interpolation

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