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Volumn 231, Issue 11, 2012, Pages 4078-4095

A guide to RBF-generated finite differences for nonlinear transport: Shallow water simulations on a sphere

Author keywords

Finite differences; Hyperbolic PDEs; Radial basis functions; RBF; RBF FD; Spherical geometry

Indexed keywords

COMPUTATIONAL EFFICIENCY; ENERGY TRANSFER; FINITE DIFFERENCE METHOD; FLOW OF FLUIDS; GALERKIN METHODS; HYPERBOLIC FUNCTIONS; RADIAL BASIS FUNCTION NETWORKS;

EID: 84859212233     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2012.01.028     Document Type: Article
Times cited : (171)

References (48)
  • 1
  • 3
    • 0016557674 scopus 로고
    • Multidimensional binary search trees used for associative searching
    • Bentley J.L. Multidimensional binary search trees used for associative searching. Commun. ACM 1975, 18:509-517.
    • (1975) Commun. ACM , vol.18 , pp. 509-517
    • Bentley, J.L.1
  • 4
    • 84857935944 scopus 로고    scopus 로고
    • A dynamic hp-adaptive discontinuous Galerkin method for shallow water flows on the sphere with application to a global tsunami simulation
    • in press, .
    • S. Blaise, A. St-Cyr, A dynamic hp-adaptive discontinuous Galerkin method for shallow water flows on the sphere with application to a global tsunami simulation, Mon. Weather Rev., in press, . http://dx.doi.org/10.1175/MWR-D-11-00038.1.
    • Mon. Weather Rev.
    • Blaise, S.1    St-Cyr, A.2
  • 5
    • 85190822772 scopus 로고    scopus 로고
    • A multi-CPU/GPU implementation of RBF-generated finite differences for PDEs on a sphere
    • Bollig E., Flyer N., Erlebacher G. A multi-CPU/GPU implementation of RBF-generated finite differences for PDEs on a sphere. AGU 2011, IN77.
    • (2011) AGU , vol.IN77
    • Bollig, E.1    Flyer, N.2    Erlebacher, G.3
  • 6
    • 85190756340 scopus 로고    scopus 로고
    • Using radial basis function finite difference (RBF-FD) for PDE solutions on the GPU
    • submitted for publication.
    • E. Bollig, N. Flyer, G. Erlebacher, Using radial basis function finite difference (RBF-FD) for PDE solutions on the GPU, J. Comput. Phys., submitted for publication.
    • J. Comput. Phys.
    • Bollig, E.1    Flyer, N.2    Erlebacher, G.3
  • 7
    • 24944461801 scopus 로고    scopus 로고
    • Analysis of discrete shallow-water models on geodesic delaunay grids with c-type staggering
    • Bonaventura L., Ringler T. Analysis of discrete shallow-water models on geodesic delaunay grids with c-type staggering. Mon. Weather Rev. 2005, 133:2351-2373.
    • (2005) Mon. Weather Rev. , vol.133 , pp. 2351-2373
    • Bonaventura, L.1    Ringler, T.2
  • 8
    • 1942539307 scopus 로고    scopus 로고
    • Numerical methods for high dimensional Hamilton-Jacobi equations using radial basis functions
    • Cecil T., Qian J., Osher S. Numerical methods for high dimensional Hamilton-Jacobi equations using radial basis functions. J. Comput. Phys. 2004, 196:327-347.
    • (2004) J. Comput. Phys. , vol.196 , pp. 327-347
    • Cecil, T.1    Qian, J.2    Osher, S.3
  • 9
    • 35248873397 scopus 로고    scopus 로고
    • Local RBF-FD solutions for steady convection-diffusion problems
    • Chandhini G., Sanyasiraju Y.V.S.S. Local RBF-FD solutions for steady convection-diffusion problems. Int. J. Numer. Methods Eng. 2007, 72:352-378.
    • (2007) Int. J. Numer. Methods Eng. , vol.72 , pp. 352-378
    • Chandhini, G.1    Sanyasiraju, Y.V.S.S.2
  • 11
    • 78149413002 scopus 로고    scopus 로고
    • Adaptive meshless centres and RBF stencils for Poisson equation
    • Davydov O., Oanh D.I. Adaptive meshless centres and RBF stencils for Poisson equation. J. Comp. Phys. 2011, 230:287-304.
    • (2011) J. Comp. Phys. , vol.230 , pp. 287-304
    • Davydov, O.1    Oanh, D.I.2
  • 12
    • 22244445528 scopus 로고    scopus 로고
    • Error estimates of local multiquadric-based differential quadrature (LMQDQ) method through numerical experiments
    • Ding H., Shu C., Tang D.B. Error estimates of local multiquadric-based differential quadrature (LMQDQ) method through numerical experiments. Int. J. Numer. Methods Eng. 2005, 63:1513-1529.
    • (2005) Int. J. Numer. Methods Eng. , vol.63 , pp. 1513-1529
    • Ding, H.1    Shu, C.2    Tang, D.B.3
  • 13
    • 0036467951 scopus 로고    scopus 로고
    • Interpolation in the limit of increasingly flat radial basis functions
    • Driscoll T.A., Fornberg B. Interpolation in the limit of increasingly flat radial basis functions. Comput. Math. Appl. 2002, 43:413-422.
    • (2002) Comput. Math. Appl. , vol.43 , pp. 413-422
    • Driscoll, T.A.1    Fornberg, B.2
  • 14
    • 35348863598 scopus 로고    scopus 로고
    • Meshless approximation methods with MATLAB
    • World Scientific Publishers, Singapore
    • Fasshauer G.E. Meshless approximation methods with MATLAB. Interdisciplinary Mathematical Sciences 2007, vol. 6. World Scientific Publishers, Singapore.
    • (2007) Interdisciplinary Mathematical Sciences , vol.6
    • Fasshauer, G.E.1
  • 15
    • 79954933248 scopus 로고    scopus 로고
    • Radial basis functions: developments and applications to planetary scale flows
    • Flyer N., Fornberg B. Radial basis functions: developments and applications to planetary scale flows. Comput. Fluids 2011, 26:23-32.
    • (2011) Comput. Fluids , vol.26 , pp. 23-32
    • Flyer, N.1    Fornberg, B.2
  • 16
    • 73649141262 scopus 로고    scopus 로고
    • Rotational transport on a sphere: local node refinement with radial basis functions
    • Flyer N., Lehto E. Rotational transport on a sphere: local node refinement with radial basis functions. J. Comput. Phys. 2010, 229:1954-1969.
    • (2010) J. Comput. Phys. , vol.229 , pp. 1954-1969
    • Flyer, N.1    Lehto, E.2
  • 17
    • 34548390120 scopus 로고    scopus 로고
    • Transport schemes on a sphere using radial basis functions
    • Flyer N., Wright G.B. Transport schemes on a sphere using radial basis functions. J. Comput. Phys. 2007, 226:1059-1084.
    • (2007) J. Comput. Phys. , vol.226 , pp. 1059-1084
    • Flyer, N.1    Wright, G.B.2
  • 18
    • 67149139433 scopus 로고    scopus 로고
    • A radial basis function method for the shallow water equations on a sphere
    • Flyer N., Wright G.B. A radial basis function method for the shallow water equations on a sphere. Proc. Roy. Soc. A 2009, 465:1949-1976.
    • (2009) Proc. Roy. Soc. A , vol.465 , pp. 1949-1976
    • Flyer, N.1    Wright, G.B.2
  • 19
    • 0036467591 scopus 로고    scopus 로고
    • Observations on the behavior of radial basis functions near boundaries
    • Fornberg B., Driscoll T.A., Wright G., Charles R. Observations on the behavior of radial basis functions near boundaries. Comput. Math. Appl. 2002, 43:473-490.
    • (2002) Comput. Math. Appl. , vol.43 , pp. 473-490
    • Fornberg, B.1    Driscoll, T.A.2    Wright, G.3    Charles, R.4
  • 20
    • 79957589881 scopus 로고    scopus 로고
    • Stable computations with gaussian radial functions
    • Fornberg B., Larsson E., Flyer N. Stable computations with gaussian radial functions. SIAM J. Sci. Comput. 2011, 33(2):869-892.
    • (2011) SIAM J. Sci. Comput. , vol.33 , Issue.2 , pp. 869-892
    • Fornberg, B.1    Larsson, E.2    Flyer, N.3
  • 21
    • 78751704720 scopus 로고    scopus 로고
    • Stabilization of RBF-generated finite difference methods for convective PDEs
    • Fornberg B., Lehto E. Stabilization of RBF-generated finite difference methods for convective PDEs. J. Comput. Phys. 2011, 230:2270-2285.
    • (2011) J. Comput. Phys. , vol.230 , pp. 2270-2285
    • Fornberg, B.1    Lehto, E.2
  • 22
    • 67149133887 scopus 로고    scopus 로고
    • A stable algorithm for flat radial basis functions on a sphere
    • Fornberg B., Piret C. A stable algorithm for flat radial basis functions on a sphere. SIAM J. Sci. Comput. 2007, 200:178-192.
    • (2007) SIAM J. Sci. Comput. , vol.200 , pp. 178-192
    • Fornberg, B.1    Piret, C.2
  • 23
    • 38549128750 scopus 로고    scopus 로고
    • On choosing a radial basis function and a shape parameter when solving a convective PDE on a sphere
    • Fornberg B., Piret C. On choosing a radial basis function and a shape parameter when solving a convective PDE on a sphere. J. Comput. Phys. 2008, 227:2758-2780.
    • (2008) J. Comput. Phys. , vol.227 , pp. 2758-2780
    • Fornberg, B.1    Piret, C.2
  • 24
    • 14644431037 scopus 로고    scopus 로고
    • Stable computation of multiquadric interpolants for all values of the shape parameter
    • Fornberg B., Wright G. Stable computation of multiquadric interpolants for all values of the shape parameter. Comput. Math. Appl. 2004, 48:853-867.
    • (2004) Comput. Math. Appl. , vol.48 , pp. 853-867
    • Fornberg, B.1    Wright, G.2
  • 25
    • 34250838673 scopus 로고    scopus 로고
    • The Runge phenomenon and spatially variable shape parameters in RBF interpolation
    • Fornberg B., Zuev J. The Runge phenomenon and spatially variable shape parameters in RBF interpolation. Comput. Math. Appl. 2007, 54:379-398.
    • (2007) Comput. Math. Appl. , vol.54 , pp. 379-398
    • Fornberg, B.1    Zuev, J.2
  • 26
    • 8744312833 scopus 로고    scopus 로고
    • An initial-value problem for testing numerical models of the global shallow-water equations
    • Galewsky J., Scott R.K., Polvani L.M. An initial-value problem for testing numerical models of the global shallow-water equations. Tellus 2004, 56A:429-440.
    • (2004) Tellus , vol.56 A , pp. 429-440
    • Galewsky, J.1    Scott, R.K.2    Polvani, L.M.3
  • 29
    • 70449093424 scopus 로고    scopus 로고
    • Diffusion experiments with a global discontinuous Galerkin shallow-water model
    • Nair R.D. Diffusion experiments with a global discontinuous Galerkin shallow-water model. Mon. Weather Rev. 2009, 137:3339-3350.
    • (2009) Mon. Weather Rev. , vol.137 , pp. 3339-3350
    • Nair, R.D.1
  • 30
    • 18544370717 scopus 로고    scopus 로고
    • A discontinuous Galerkin global shallow water model
    • Nair R.D., Thomas S.J., Loft R.D. A discontinuous Galerkin global shallow water model. Mon. Weather Rev. 2005, 133:876-888.
    • (2005) Mon. Weather Rev. , vol.133 , pp. 876-888
    • Nair, R.D.1    Thomas, S.J.2    Loft, R.D.3
  • 31
    • 78651429874 scopus 로고    scopus 로고
    • On numerical solution of the shallow water equations with chemical reactions on icosahedral geodesic grid
    • Pudykiewicz J.A. On numerical solution of the shallow water equations with chemical reactions on icosahedral geodesic grid. J. Comput. Phys. 2011, 230:1956-1991.
    • (2011) J. Comput. Phys. , vol.230 , pp. 1956-1991
    • Pudykiewicz, J.A.1
  • 32
    • 44649201430 scopus 로고    scopus 로고
    • Application of local MQ-DQ method to solve 3D incompressible viscous flows with curved boundary
    • Shan Y.Y., Shu C., Lu Z.L. Application of local MQ-DQ method to solve 3D incompressible viscous flows with curved boundary. Comput. Model. Eng. Sci. 2008, 25:99-113.
    • (2008) Comput. Model. Eng. Sci. , vol.25 , pp. 99-113
    • Shan, Y.Y.1    Shu, C.2    Lu, Z.L.3
  • 33
    • 0037436111 scopus 로고    scopus 로고
    • Local radial basis function-based differential quadrature method and its application to solve two-dimensional incompressible Navier-Stokes equations
    • Shu C., Ding H., Yeo K.S. Local radial basis function-based differential quadrature method and its application to solve two-dimensional incompressible Navier-Stokes equations. Comput. Methods Appl. Mech. Eng. 2003, 192:941-954.
    • (2003) Comput. Methods Appl. Mech. Eng. , vol.192 , pp. 941-954
    • Shu, C.1    Ding, H.2    Yeo, K.S.3
  • 34
    • 0000007535 scopus 로고    scopus 로고
    • Fast shallow water equation solvers in latitude-longitude coordinates
    • Spotz W.F., Taylor M.A., Swarztrauber P.N. Fast shallow water equation solvers in latitude-longitude coordinates. J. Comput. Phys. 1998, 145:432-444.
    • (1998) J. Comput. Phys. , vol.145 , pp. 432-444
    • Spotz, W.F.1    Taylor, M.A.2    Swarztrauber, P.N.3
  • 35
  • 36
    • 67349112089 scopus 로고    scopus 로고
    • The use of PDE centers in the local RBF Hermitean method for 3D convective-diffusion problems
    • Stevens D., Power H., Lees M., Morvan H. The use of PDE centers in the local RBF Hermitean method for 3D convective-diffusion problems. J. Comput. Phys. 2009, 228:4606-4624.
    • (2009) J. Comput. Phys. , vol.228 , pp. 4606-4624
    • Stevens, D.1    Power, H.2    Lees, M.3    Morvan, H.4
  • 37
    • 0024228126 scopus 로고
    • Effects of using a posteriori methods for the conservation of integral invariants
    • Takacs L.L. Effects of using a posteriori methods for the conservation of integral invariants. Mon. Weather Rev. 1988, 116:525-545.
    • (1988) Mon. Weather Rev. , vol.116 , pp. 525-545
    • Takacs, L.L.1
  • 38
    • 0030640666 scopus 로고    scopus 로고
    • The spectral element method for the shallow water equations on the sphere
    • Taylor M., Tribbia J., Iskandarani M. The spectral element method for the shallow water equations on the sphere. J. Comput. Phys. 1997, 130:92-108.
    • (1997) J. Comput. Phys. , vol.130 , pp. 92-108
    • Taylor, M.1    Tribbia, J.2    Iskandarani, M.3
  • 39
    • 0034079274 scopus 로고    scopus 로고
    • Numerical simulation of Rossby-Haurwitz waves
    • Thuburn J., Li Y. Numerical simulation of Rossby-Haurwitz waves. Tellus 2000, 52A:181-189.
    • (2000) Tellus , vol.52 A , pp. 181-189
    • Thuburn, J.1    Li, Y.2
  • 40
    • 3042722159 scopus 로고    scopus 로고
    • On using radial basis functions in a " finite difference mode" with applications to elasticity problems
    • Tolstykh A.I. On using radial basis functions in a " finite difference mode" with applications to elasticity problems. Comput. Mech. 2003, 33:68-79.
    • (2003) Comput. Mech. , vol.33 , pp. 68-79
    • Tolstykh, A.I.1
  • 41
    • 3042836772 scopus 로고    scopus 로고
    • On using RBF-based differencing formulas for unstructured and mixed structured-unstructured grid calculations
    • Lausanne
    • 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, vol. 228, Lausanne, 2000, pp. 4606-4624.
    • (2000) Proceedings of the 16th IMACS World Congress , vol.228 , pp. 4606-4624
    • Tolstykh, A.I.1
  • 42
    • 85066350454 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., Swarztrauber P.N. A standard test set for numerical approximations to the shallow water equations in spherical geometry. J. Comput. Phys. 1992, 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
  • 43
    • 0035640976 scopus 로고    scopus 로고
    • How good can polynomial interpolation on the sphere be?
    • Womersley R.S., Sloan I.H. How good can polynomial interpolation on the sphere be?. Adv. Comput. Math. 2001, 23:195-226.
    • (2001) Adv. Comput. Math. , vol.23 , pp. 195-226
    • Womersley, R.S.1    Sloan, I.H.2
  • 44
    • 85190783157 scopus 로고    scopus 로고
    • Interpolation and cubature on the sphere, Website
    • R.S. Womersley, I.H. Sloan, Interpolation and cubature on the sphere, Website, 2003, . http://web.maths.unsw.edu.au.
    • (2003)
    • Womersley, R.S.1    Sloan, I.H.2
  • 45
    • 85190808105 scopus 로고    scopus 로고
    • Radial basis function interpolation: numerical and analytical developments, Ph.D. thesis, University of Colorado, Boulder
    • G.B. Wright, Radial basis function interpolation: numerical and analytical developments, Ph.D. thesis, University of Colorado, Boulder, 2003.
    • (2003)
    • Wright, G.B.1
  • 46
    • 78751702068 scopus 로고    scopus 로고
    • A hybrid radial basis function - pseudospectral method for thermal convection in a 3D spherical shell
    • Wright G.B., Flyer N., Yuen D.A. A hybrid radial basis function - pseudospectral method for thermal convection in a 3D spherical shell. Geophys. Geochem. Geosyst. 2010, 11(7):Q07003.
    • (2010) Geophys. Geochem. Geosyst. , vol.11 , Issue.7
    • Wright, G.B.1    Flyer, N.2    Yuen, D.A.3
  • 47
    • 29144437684 scopus 로고    scopus 로고
    • Scattered node compact finite difference-type formulas generated from radial basis functions
    • Wright G.B., Fornberg B. Scattered node compact finite difference-type formulas generated from radial basis functions. J. Comput. Phys. 2006, 212:99-123.
    • (2006) J. Comput. Phys. , vol.212 , pp. 99-123
    • Wright, G.B.1    Fornberg, B.2
  • 48
    • 79951514320 scopus 로고    scopus 로고
    • Parallel multilevel methods for implicit solution of shallow water equations with nonsmooth topography on the cubed-sphere
    • Yang C., Cai X.C. Parallel multilevel methods for implicit solution of shallow water equations with nonsmooth topography on the cubed-sphere. J. Comput. Phys. 2011, 230:2523-2539.
    • (2011) J. Comput. Phys. , vol.230 , pp. 2523-2539
    • Yang, C.1    Cai, X.C.2


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