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Volumn 65, Issue 4, 2013, Pages 627-637

Stable calculation of Gaussian-based RBF-FD stencils

Author keywords

Gaussians; Ill conditioning; Radial basis functions; RBF; RBF FD; RBF GA

Indexed keywords

GAUSSIANS; ILL-CONDITIONING; RADIAL BASIS FUNCTIONS; RBF; RBF-FD; RBF-GA;

EID: 84873200862     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2012.11.006     Document Type: Article
Times cited : (205)

References (28)
  • 1
    • 0032166374 scopus 로고    scopus 로고
    • Calculation of weights in finite difference formulas
    • B. Fornberg Calculation of weights in finite difference formulas SIAM Rev. 40 3 1998 685 691
    • (1998) SIAM Rev. , vol.40 , Issue.3 , pp. 685-691
    • Fornberg, B.1
  • 2
    • 0036467951 scopus 로고    scopus 로고
    • Interpolation in the limit of increasingly flat radial basis functions
    • T.A. Driscoll, and B. Fornberg Interpolation in the limit of increasingly flat radial basis functions Comput. Math. Appl. 43 2002 413 422
    • (2002) Comput. Math. Appl. , vol.43 , pp. 413-422
    • Driscoll, T.A.1    Fornberg, B.2
  • 3
    • 0037436111 scopus 로고    scopus 로고
    • Local radial basis function-based differential quadrature method and its application to solve two-dimensional incompressible Navier-Stokes equations
    • C. Shu, H. Ding, and K.S. Yeo Local radial basis function-based differential quadrature method and its application to solve two-dimensional incompressible Navier-Stokes equations Comput. Methods Appl. Mech. Eng. 192 2003 941 954
    • (2003) Comput. Methods Appl. Mech. Eng. , vol.192 , pp. 941-954
    • Shu, C.1    Ding, H.2    Yeo, K.S.3
  • 4
    • 3042836772 scopus 로고    scopus 로고
    • On using RBF-based differencing formulas for unstructured and mixed structured-unstructured grid calculations
    • A.I. Tolstykh, On using RBF-based differencing formulas for unstructured and mixed structured-unstructured grid calculations, in: Proceedings of the 16th IMACS World Congress, Lausanne, 2000.
    • (2000) Proceedings of the 16th IMACS World Congress, Lausanne
    • Tolstykh, A.I.1
  • 5
    • 3042722159 scopus 로고    scopus 로고
    • On using radial basis functions in a finite difference mode with applications to elasticity problems
    • A.I. Tolstykh, and D.A. Shirobokov On using radial basis functions in a finite difference mode with applications to elasticity problems Comput. Mech. 33 2003 68 79
    • (2003) Comput. Mech. , vol.33 , pp. 68-79
    • Tolstykh, A.I.1    Shirobokov, D.A.2
  • 6
    • 17944381991 scopus 로고    scopus 로고
    • Theoretical and computational aspects of multivariate interpolation with increasingly flat radial basis functions
    • E. Larsson, and B. Fornberg Theoretical and computational aspects of multivariate interpolation with increasingly flat radial basis functions Comput. Math. Appl. 49 2005 103 130
    • (2005) Comput. Math. Appl. , vol.49 , pp. 103-130
    • Larsson, E.1    Fornberg, B.2
  • 7
    • 0942300715 scopus 로고    scopus 로고
    • Some observations regarding interpolants in the limit of flat radial basis functions
    • B. Fornberg, G. Wright, and E. Larsson Some observations regarding interpolants in the limit of flat radial basis functions Comput. Math. Appl. 47 2004 37 55
    • (2004) Comput. Math. Appl. , vol.47 , pp. 37-55
    • Fornberg, B.1    Wright, G.2    Larsson, E.3
  • 8
    • 21244456148 scopus 로고    scopus 로고
    • Multivariate interpolation by polynomials and radial basis functions
    • R. Schaback Multivariate interpolation by polynomials and radial basis functions Constr. Approx. 21 2005 293 317
    • (2005) Constr. Approx. , vol.21 , pp. 293-317
    • Schaback, R.1
  • 9
    • 38549128750 scopus 로고    scopus 로고
    • On choosing a radial basis function and a shape parameter when solving a convective PDE on a sphere
    • B. Fornberg, and C. Piret On choosing a radial basis function and a shape parameter when solving a convective PDE on a sphere J. Comput. Phys. 227 2008 2758 2780
    • (2008) J. Comput. Phys. , vol.227 , pp. 2758-2780
    • Fornberg, B.1    Piret, C.2
  • 10
    • 0242667184 scopus 로고    scopus 로고
    • A numerical study of some radial basis function based solution methods for elliptic PDEs
    • E. Larsson, and B. Fornberg A numerical study of some radial basis function based solution methods for elliptic PDEs Comput. Math. Appl. 46 2003 891 902
    • (2003) Comput. Math. Appl. , vol.46 , pp. 891-902
    • Larsson, E.1    Fornberg, B.2
  • 11
    • 29144437684 scopus 로고    scopus 로고
    • Scattered node compact finite difference-type formulas generated from radial basis functions
    • G.B. Wright, and B. Fornberg Scattered node compact finite difference-type formulas generated from radial basis functions J. Comput. Phys. 212 2006 99 123
    • (2006) J. Comput. Phys. , vol.212 , pp. 99-123
    • Wright, G.B.1    Fornberg, B.2
  • 12
    • 14644431037 scopus 로고    scopus 로고
    • Stable computation of multiquadric interpolants for all values of the shape parameter
    • B. Fornberg, and G. Wright Stable computation of multiquadric interpolants for all values of the shape parameter Comput. Math. Appl. 48 2004 853 867
    • (2004) Comput. Math. Appl. , vol.48 , pp. 853-867
    • Fornberg, B.1    Wright, G.2
  • 14
    • 44649201430 scopus 로고    scopus 로고
    • Application of local MQ-DQ method to solve 3D incompressible viscous flows with curved boundary
    • Y.Y. Shan, C. Shu, and Z.L. Lu Application of local MQ-DQ method to solve 3D incompressible viscous flows with curved boundary CMES Comput. Model. Eng. Sci. 25 2008 99 113
    • (2008) CMES Comput. Model. Eng. Sci. , vol.25 , pp. 99-113
    • Shan, Y.Y.1    Shu, C.2    Lu, Z.L.3
  • 15
    • 67349112089 scopus 로고    scopus 로고
    • The use of PDE centers in the local RBF Hermitian method for 3D convective-diffusion problems
    • D. Stevens, H. Power, M. Lees, and H. Morvan The use of PDE centers in the local RBF Hermitian method for 3D convective-diffusion problems J. Comput. Phys. 228 2009 4606 4624
    • (2009) J. Comput. Phys. , vol.228 , pp. 4606-4624
    • Stevens, D.1    Power, H.2    Lees, M.3    Morvan, H.4
  • 16
    • 84859212233 scopus 로고    scopus 로고
    • A guide to RBF-generated finite differences for nonlinear transport: Shallow water simulations on a sphere
    • N. Flyer, E. Lehto, S. Blaise, G.B. Wright, and A. St-Cyr A guide to RBF-generated finite differences for nonlinear transport: shallow water simulations on a sphere J. Comput. Phys. 231 2012 4078 4095
    • (2012) J. Comput. Phys. , vol.231 , pp. 4078-4095
    • Flyer, N.1    Lehto, E.2    Blaise, S.3    Wright, G.B.4    St-Cyr, A.5
  • 17
    • 78751704720 scopus 로고    scopus 로고
    • Stabilization of RBF-generated finite difference methods for convective PDEs
    • B. Fornberg, and E. Lehto Stabilization of RBF-generated finite difference methods for convective PDEs J. Comput. Phys. 230 2011 2270 2285
    • (2011) J. Comput. Phys. , vol.230 , pp. 2270-2285
    • Fornberg, B.1    Lehto, E.2
  • 20
    • 38549125605 scopus 로고    scopus 로고
    • A stable algorithm for radial basis functions on a sphere
    • B. Fornberg, and C. Piret A stable algorithm for radial basis functions on a sphere SIAM J. Sci. Comput. 30 2007 60 80
    • (2007) SIAM J. Sci. Comput. , vol.30 , pp. 60-80
    • Fornberg, B.1    Piret, C.2
  • 21
    • 84860446897 scopus 로고    scopus 로고
    • Stable evaluation of Gaussian RBF interpolants
    • G.E. Fasshauer, and M.J. McCourt Stable evaluation of Gaussian RBF interpolants SIAM J. Sci. Comput. 34 2 2012 A737 A762
    • (2012) SIAM J. Sci. Comput. , vol.34 , Issue.2
    • Fasshauer, G.E.1    McCourt, M.J.2
  • 22
    • 79957589881 scopus 로고    scopus 로고
    • Stable computations with Gaussian radial basis functions
    • B. Fornberg, E. Larsson, and N. Flyer Stable computations with Gaussian radial basis functions SIAM J. Sci. Comput. 33 2011 869 892
    • (2011) SIAM J. Sci. Comput. , vol.33 , pp. 869-892
    • Fornberg, B.1    Larsson, E.2    Flyer, N.3
  • 24
    • 33745894671 scopus 로고    scopus 로고
    • A new class of oscillatory radial basis functions
    • B. Fornberg, E. Larsson, and G. Wright A new class of oscillatory radial basis functions Comput. Math. Appl. 51 2006 1209 1222
    • (2006) Comput. Math. Appl. , vol.51 , pp. 1209-1222
    • Fornberg, B.1    Larsson, E.2    Wright, G.3
  • 25
    • 85140870434 scopus 로고    scopus 로고
    • Stable computation of differentiation matrices and scattered node stencils based on Gaussian radial basis functions
    • (submitted for publication)
    • E. Larsson, E. Lehto, A.R.H. Heryudono, B. Fornberg, Stable computation of differentiation matrices and scattered node stencils based on Gaussian radial basis functions, SIAM J. Sci. Comput. (submitted for publication).
    • SIAM J. Sci. Comput.
    • Larsson, E.1    Lehto, E.2    Heryudono, A.R.H.3    Fornberg, B.4
  • 26
    • 80052262924 scopus 로고    scopus 로고
    • On the optimal shape parameter for Gaussian radial basis function finite difference approximation of the Poisson equation
    • O. Davydov, and D.T. Oanh On the optimal shape parameter for Gaussian radial basis function finite difference approximation of the Poisson equation Comput. Math. Appl. 62 2011 2143 2161
    • (2011) Comput. Math. Appl. , vol.62 , pp. 2143-2161
    • Davydov, O.1    Oanh, D.T.2
  • 27
    • 34250838673 scopus 로고    scopus 로고
    • The Runge phenomenon and spatially variable shape parameters in RBF interpolation
    • B. Fornberg, and J. Zuev The Runge phenomenon and spatially variable shape parameters in RBF interpolation Comput. Math. Appl. 54 2007 379 398
    • (2007) Comput. Math. Appl. , vol.54 , pp. 379-398
    • Fornberg, B.1    Zuev, J.2


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