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Volumn 62, Issue 5, 2011, Pages 2143-2161

On the optimal shape parameter for Gaussian radial basis function finite difference approximation of the Poisson equation

Author keywords

Meshless methods; RBF FD

Indexed keywords

DIRICHLET PROBLEM; FINITE DIFFERENCE; FINITE DIFFERENCE APPROXIMATIONS; GAUSSIAN RADIAL BASIS FUNCTIONS; GAUSSIANS; MESH-LESS METHODS; MESHLESS; MULTILEVEL ALGORITHM; NUMERICAL EXPERIMENTS; OPTIMAL SHAPE; RBF-FD; SHAPE PARAMETERS; SMOOTH SOLUTIONS;

EID: 80052262924     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2011.06.037     Document Type: Article
Times cited : (70)

References (16)
  • 2
    • 58249141995 scopus 로고    scopus 로고
    • Truncated Gaussian RBF differences are always inferior to finite differences of the same stencil width
    • J.P. Boyd, and L. Wang Truncated Gaussian RBF differences are always inferior to finite differences of the same stencil width Commun. Comput. Phys. 5 2009 42 60
    • (2009) Commun. Comput. Phys. , vol.5 , pp. 42-60
    • Boyd, J.P.1    Wang, L.2
  • 3
    • 78149413002 scopus 로고    scopus 로고
    • Adaptive meshless centres and RBF stencils for Poisson equation
    • O. Davydov, and D.T. Oanh Adaptive meshless centres and RBF stencils for Poisson equation J. Comput. Phys. 230 2011 287 304
    • (2011) J. Comput. Phys. , vol.230 , pp. 287-304
    • Davydov, O.1    Oanh, D.T.2
  • 4
    • 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
  • 5
    • 0038604335 scopus 로고    scopus 로고
    • Local multiquadric approximation for solving boundary value problems
    • C.K. Lee, X. Liu, and S.C. Fan Local multiquadric approximation for solving boundary value problems Comput. Mech. 30 56 2003 396 409
    • (2003) Comput. Mech. , vol.30 , Issue.56 , pp. 396-409
    • Lee, C.K.1    Liu, X.2    Fan, S.C.3
  • 6
    • 0037436111 scopus 로고    scopus 로고
    • Local radial basis funcion-based differential quadrature method and its application to solve two-dimensional incompressible Navier-Stokes equations
    • DOI 10.1016/S0045-7825(02)00618-7, PII S0045782502006187
    • C. Shu, H. Ding, and K.S. Yeo Local radial basis function-based differential quadrature method and its application to solve two-dimensional incompressible NavierStokes equations Comput. Methods Appl. Mech. Eng. 192 78 2003 941 954 (Pubitemid 36225326)
    • (2003) Computer Methods in Applied Mechanics and Engineering , vol.192 , Issue.7-8 , pp. 941-954
    • Shu, C.1    Ding, H.2    Yeo, K.S.3
  • 7
    • 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 1 2003 68 79
    • (2003) Comput. Mech. , vol.33 , Issue.1 , pp. 68-79
    • Tolstykh, A.I.1    Shirobokov, D.A.2
  • 8
    • 29144437684 scopus 로고    scopus 로고
    • Scattered node compact finite difference-type formulas generated from radial basis functions
    • DOI 10.1016/j.jcp.2005.05.030, PII S0021999105003116
    • G.B. Wright, and B. Fornberg Scattered node compact finite difference-type formulas generated from radial basis functions J. Comput. Phys. 212 1 2006 99 123 (Pubitemid 41799807)
    • (2006) Journal of Computational Physics , vol.212 , Issue.1 , pp. 99-123
    • Wright, G.B.1    Fornberg, B.2
  • 9
    • 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 2 2011 869 892
    • (2011) SIAM J. Sci. Comput. , vol.33 , Issue.2 , pp. 869-892
    • Fornberg, B.1    Larsson, E.2    Flyer, N.3
  • 10
    • 38549125605 scopus 로고    scopus 로고
    • A stable algorithm for flat radial basis functions on a sphere
    • B. Fornberg, and C. Piret A stable algorithm for flat 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
  • 11
    • 14644431037 scopus 로고    scopus 로고
    • Stable computation of multiquadric interpolants for all values of the shape parameter
    • DOI 10.1016/j.camwa.2003.08.010, PII S0898122104003190
    • B. Fornberg, and G. Wright Stable computation of multiquadric interpolants for all values of the shape parameter Comput. Math. Appl. 48 2004 853 867 (Pubitemid 40319740)
    • (2004) Computers and Mathematics with Applications , vol.48 , Issue.5-6 , pp. 853-867
    • Fornberg, B.1    Wright, G.2
  • 13
    • 34250838673 scopus 로고    scopus 로고
    • The Runge phenomenon and spatially variable shape parameters in RBF interpolation
    • DOI 10.1016/j.camwa.2007.01.028, PII S0898122107002210
    • B. Fornberg, and J. Zuev The Runge phenomenon and spatially variable shape parameters in RBF interpolation Comput. Math. Appl. 54 2007 379 398 (Pubitemid 46977176)
    • (2007) Computers and Mathematics with Applications , vol.54 , Issue.3 , pp. 379-398
    • Fornberg, B.1    Zuev, J.2
  • 14
    • 3042799255 scopus 로고    scopus 로고
    • Cambridge University Press New York, NY, USA
    • M.D. Buhmann Radial Basis Functions 2003 Cambridge University Press New York, NY, USA
    • (2003) Radial Basis Functions
    • Buhmann, M.D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.