메뉴 건너뛰기




Volumn 13, Issue 6, 2007, Pages 643-663

Divergence-free RBFs on surfaces

Author keywords

Incompressible fluid; Numerical modeling; Radial basis function; Sphere; Vector fields

Indexed keywords


EID: 35548941391     PISSN: 10695869     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00041-006-6903-2     Document Type: Article
Times cited : (29)

References (32)
  • 2
    • 15844363062 scopus 로고    scopus 로고
    • Radial Basis Functions: Theory and Implementations
    • of, Cambridge University Press, Cambridge
    • Buhmann, M. D. Radial Basis Functions: Theory and Implementations, Vol. 12 of Cambridge Monographs on Applied and Computational Mathematics, Cambridge University Press, Cambridge, (2003).
    • (2003) Cambridge Monographs on Applied and Computational Mathematics , vol.12
    • Buhmann, M.D.1
  • 3
    • 0036467951 scopus 로고    scopus 로고
    • Interpolation in the limit of increasingly flat radial basis functions
    • Driscoll, T. A. and Fornberg, B. (2002). Interpolation in the limit of increasingly flat radial basis functions, Comput. Math. Appl. 43, 413-422.
    • (2002) Comput. Math. Appl , vol.43 , pp. 413-422
    • Driscoll, T.A.1    Fornberg, B.2
  • 5
    • 35548959967 scopus 로고    scopus 로고
    • A stable algorithm for flat radial basis functions on a sphere
    • to be submitted
    • Fornberg, B. and Piret, C. (2006). A stable algorithm for flat radial basis functions on a sphere, to be submitted.
    • (2006)
    • Fornberg, B.1    Piret, C.2
  • 6
    • 14644431037 scopus 로고    scopus 로고
    • Stable computation of multiquadric interpolants for all values of the shape parameter
    • Fornberg, B. and Wright, G. (2004). Stable computation of multiquadric interpolants for all values of the shape parameter, Comput. Math. Appl. 48, 853-867.
    • (2004) Comput. Math. Appl , vol.48 , pp. 853-867
    • Fornberg, B.1    Wright, G.2
  • 7
    • 35548936844 scopus 로고    scopus 로고
    • Improved stability estimates and a characterization of the native space for marix-valued RBFs
    • preprint
    • Fuselier, E. (2006). Improved stability estimates and a characterization of the native space for marix-valued RBFs, preprint.
    • (2006)
    • Fuselier, E.1
  • 8
    • 35548932402 scopus 로고    scopus 로고
    • Sobolev-type approximation rates for divergence-free and curl-free RBF interpolants
    • preprint
    • Fuselier, E. (2006). Sobolev-type approximation rates for divergence-free and curl-free RBF interpolants, preprint.
    • (2006)
    • Fuselier, E.1
  • 11
    • 0033402208 scopus 로고    scopus 로고
    • Correlation functions for atmospheric data analysis
    • Gneiting, T. (1999). Correlation functions for atmospheric data analysis, Q. J. R. Meteorol. Soc. 125, 2449-2464.
    • (1999) Q. J. R. Meteorol. Soc , vol.125 , pp. 2449-2464
    • Gneiting, T.1
  • 12
    • 27844497928 scopus 로고    scopus 로고
    • Discretizing manifolds via minimum energy points
    • Hardin, D. P. and Saff, E. B. (2004). Discretizing manifolds via minimum energy points, Notices Amer. Math. Soc. 51, 1186-1194.
    • (2004) Notices Amer. Math. Soc , vol.51 , pp. 1186-1194
    • Hardin, D.P.1    Saff, E.B.2
  • 13
    • 0001018295 scopus 로고
    • Multiquadric equations of topograpy and other irregular surfaces
    • Hardy, R. L. (1971). Multiquadric equations of topograpy and other irregular surfaces, J. Geophy. Res. 76, 1905-1915.
    • (1971) J. Geophy. Res , vol.76 , pp. 1905-1915
    • Hardy, R.L.1
  • 15
    • 3042855065 scopus 로고    scopus 로고
    • p-error estimates for radial basis function interpolation on the sphere
    • p-error estimates for radial basis function interpolation on the sphere, J. Approx. Theory 129, 58-77.
    • (2004) J. Approx. Theory , vol.129 , pp. 58-77
    • Hubbert, S.1    Morton, T.2
  • 16
    • 15544362032 scopus 로고    scopus 로고
    • Multiresolution Methods in Scattered Data Modelling
    • of, Springer-Verlag, Heidelberg
    • Iske, A. Multiresolution Methods in Scattered Data Modelling, Vol. 37 of Lecture Notes in Computational Science and Engineering, Springer-Verlag, Heidelberg, (2004).
    • (2004) Lecture Notes in Computational Science and Engineering , vol.37
    • Iske, A.1
  • 17
    • 0040118904 scopus 로고    scopus 로고
    • Error estimates for scattered data interpolation on spheres
    • Jetter, K., Stöckler, J., and Ward, J. D. (1999). Error estimates for scattered data interpolation on spheres, Math. Comput. 68, 733-747.
    • (1999) Math. Comput , vol.68 , pp. 733-747
    • Jetter, K.1    Stöckler, J.2    Ward, J.D.3
  • 18
    • 17944381991 scopus 로고    scopus 로고
    • Theoretical and computational aspects of multivariate interpolation with increasingly flat radial basis functions
    • Larsson, E. and Fornberg, B. (2005). Theoretical and computational aspects of multivariate interpolation with increasingly flat radial basis functions, Comput. Math. Appl. 49, 103-130.
    • (2005) Comput. Math. Appl , vol.49 , pp. 103-130
    • Larsson, E.1    Fornberg, B.2
  • 19
    • 29744452340 scopus 로고    scopus 로고
    • Error estimates for matrix-valued radial basis function interpolation
    • Lowitzsch, S. (2005). Error estimates for matrix-valued radial basis function interpolation, J. Approx. Theory 137, 238-249.
    • (2005) J. Approx. Theory , vol.137 , pp. 238-249
    • Lowitzsch, S.1
  • 20
    • 33646742733 scopus 로고    scopus 로고
    • Matrix-valued radial basis functions: Stability estimates and applications
    • Lowitzsch, S. (2005). Matrix-valued radial basis functions: Stability estimates and applications, Adv. Comput. Math. 23, 299-315.
    • (2005) Adv. Comput. Math , vol.23 , pp. 299-315
    • Lowitzsch, S.1
  • 21
    • 84966244353 scopus 로고
    • Multivariate interpolation and conditionally positive definite functions II
    • Madych, W.R. and Nelson, S.A. (1990). Multivariate interpolation and conditionally positive definite functions II, Math. Comp. 54, 211-230.
    • (1990) Math. Comp , vol.54 , pp. 211-230
    • Madych, W.R.1    Nelson, S.A.2
  • 22
    • 0002299145 scopus 로고
    • Spatial Variation
    • of, Springer-Verlag, Heidelberg, 2nd ed
    • Matérn, B. Spatial Variation, Vol. 36 of Lecture Notes in Statistics, Springer-Verlag, Heidelberg, 2nd ed., (1986).
    • (1986) Lecture Notes in Statistics , vol.36
    • Matérn, B.1
  • 23
    • 84968510026 scopus 로고
    • Generalized Hermite interpolation via matrix-valued conditionally positive definite functions
    • Narcowich, F. J. and Ward, J. D. (1994). Generalized Hermite interpolation via matrix-valued conditionally positive definite functions, Math. Comp. 63, 661-687.
    • (1994) Math. Comp , vol.63 , pp. 661-687
    • Narcowich, F.J.1    Ward, J.D.2
  • 24
    • 0033434521 scopus 로고    scopus 로고
    • An algorithm for selecting a good value for the parameter c in radial basis function interpolation
    • Rippa, S. (1999). An algorithm for selecting a good value for the parameter c in radial basis function interpolation, Adv. Comput. Math. 11, 193-210.
    • (1999) Adv. Comput. Math , vol.11 , pp. 193-210
    • Rippa, S.1
  • 25
    • 0031542184 scopus 로고    scopus 로고
    • Distributing many points on a sphere
    • Saff, E. B. and Kuijlaars, A. B. J. (1997). Distributing many points on a sphere, Math. Intelligencer 19, 5-11.
    • (1997) Math. Intelligencer , vol.19 , pp. 5-11
    • Saff, E.B.1    Kuijlaars, A.B.J.2
  • 26
    • 51249166702 scopus 로고
    • Error estimates and condition numbers for radial basis function interpolants
    • Schaback, R. (1995). Error estimates and condition numbers for radial basis function interpolants, Adv. Comput. Math. 3, 251-264.
    • (1995) Adv. Comput. Math , vol.3 , pp. 251-264
    • Schaback, R.1
  • 27
    • 0001743201 scopus 로고
    • Metric spaces and completely monotone functions
    • Schoenberg, I. J. (1938). Metric spaces and completely monotone functions, Ann. Math. 39, 811-841.
    • (1938) Ann. Math , vol.39 , pp. 811-841
    • Schoenberg, I.J.1
  • 28
    • 1942431755 scopus 로고
    • Conditionally positive definite functions and their application to multivariate interpolations
    • Sun, X. (1993). Conditionally positive definite functions and their application to multivariate interpolations, J. Approx. Theory 74, 159-180.
    • (1993) J. Approx. Theory , vol.74 , pp. 159-180
    • Sun, X.1
  • 29
    • 0001365249 scopus 로고
    • The approximation of vector functions and their derivatives on the sphere
    • Swarztrauber, P. N. (1981). The approximation of vector functions and their derivatives on the sphere, SIAM J. Numer. Anal. 18, 191-210.
    • (1981) SIAM J. Numer. Anal , vol.18 , pp. 191-210
    • Swarztrauber, P.N.1
  • 31
    • 0001440358 scopus 로고
    • A standard test set for numerical approximations to the shallow water equations in spherical geometry
    • Williamson, D.L., Drake, J.B., Hack, J. J., Jakob, R., and Swarztrauber, P.N. (1992). A standard test set for numerical approximations to the shallow water equations in spherical geometry, J. Comput. Phys. 102, 211-224.
    • (1992) J. Comput. Phys , vol.102 , pp. 211-224
    • Williamson, D.L.1    Drake, J.B.2    Hack, J.J.3    Jakob, R.4    Swarztrauber, P.N.5


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.