Spectral radial basis functions for full sphere computations

Journal of Computational Physics

Volumn 227, Issue 2, 2007, Pages 1209-1224

  Livermore, Philip W ^a   Jones, Chris A ^a   Worland, Steven J ^b  

^a UNIVERSITY OF LEEDS   (United Kingdom)

^b UNIVERSITY OF EXETER   (United Kingdom)

Author keywords

Chebyshev polynomial; Coordinate singularity; Jacobi polynomials; Polar coordinates; Spectral method

Indexed keywords

POLYNOMIALS; RADIAL BASIS FUNCTION NETWORKS;

BASE FUNCTION; CHEBYSHEV POLYNOMIALS; COORDINATE SINGULARITY; DIFFERENTIABILITY; FAST TRANSFORM; JACOBI POLYNOMIALS; ONE-SIDED JACOBI; POLAR COORDINATE; RADIAL BASIS; SPECTRAL METHODS;

CHEBYSHEV POLYNOMIALS;

EID: 36148929484     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2007.08.026     Document Type: Article

References (29)

1. Boyd J.P. Chebyshev and Fourier Spectral Methods (2001), Dover
2. Backus G., Parker R., and Constable C. Foundations of Geomagnetism (1996), CUP
3. Eisen H., Heinrichs W., and Witsch K. Spectral collocation methods and polar coordinate singularities. J. Comput. Phys. 96 (1991) 241-257
4. Kerswell R.R., and Davey A. On the linear instability of elliptic pipe flow. J. Fluid Mech. 316 (1996) 307-324
5. Gottlieb D., and Orszag S. Numerical Analysis of Spectral Methods; Theory and Applications. twenty-sixth ed. CBMS-NSF Regional Conference Series in Applied Mathematics (1977), SIAM, Philadephia, PA
6. Torres D.J., and Coutsias E.A. Pseudospectral solution of the two-dimensional Navier-Stokes equations in a disk. SIAM J. Sci. Comput. 21 1 (1999) 378-402
7. Shen J. Efficient spectral-Galerkin methods III: polar and cylindrical geometries. SIAM J. Sci. Comput. 18 6 (1997) 1583-1604
8. Livermore P.W., and Jackson A. On magnetic energy instability in spherical stationary flows. Proc. Roy. Soc. A 460 (2004) 1453-1476
9. Mohseni K., and Colonius T. Numerical treatment of polar coordinate singularities. J. Comput. Phys. 157 (2000) 787-795
10. Huang W., and Sloan D.M. Pole condition for singular problems: the pseudospectral approximation. J. Comput. Phys. 107 (1993) 254-261
11. Heinrichs W. Spectral collocation schemes on the unit disk. J. Comput. Phys. 199 (2004) 66-86
12. Fornberg B. A Practical Guide to Pseudospectral Methods (1998), CUP
13. Canuto C., Hussaini M.Y., Quarteroni A., and Zang T.A. Spectral Methods for Fluid Dynamics (1988), Springer-Verlag
14. S. Worland, Magnetoconvection in Rapidly Rotating Spheres, PhD Thesis, University of Exeter, 2004.
15. Li S., and Montgomery D. Decaying two-dimensional turbulence with rigid walls. Phys. Lett. A 218 (1996) 281-291
16. Livermore P.W., and Jackson A. A comparison of numerical schemes to solve the magnetic induction eigenvalue problem in a spherical geometry. Geophys. Astrophys. Fluid Dyn. 99 6 (2005) 467-480
17. Zhang K., Liao X., and Earnshaw P. The Poincaré equation: A new polynomial and its unusual properties. J. Math. Phys. 45 12 (2004) 4777-4790
18. Verkley W.T.M. A spectral model for two-dimensional incompressible fluid flow in a circular basin. J. Comput. Phys. 136 (1997) 100-114
19. Matsushima T., and Marcus P.S. A spectral method for polar coordinates. J. Comput. Phys. 120 (1995) 365-374
20. Driscoll J.R., Healy D.M.J., and Rockmore D.N. Fast discrete polynomial transforms with applications to data analysis for distance transitive graphs. SIAM J. Comput. 26 4 (1997) 1066-1099
21. Suda R., and Takami M. A fast spherical harmonics transform algorithm. Math. Comput. 71 (2002) 703-715
22. Healy D.M.J., Rockmore D.N., Kostelec P.J., and Moore S. FFTs for the 2-sphere - improvements and variations. J. Fourier Anal. Appl. 9 4 (2003) 341-385
23. Livermore P.W., and Jackson A. Transient magnetic energy growth in spherical stationary flows. Proc. Roy. Soc. A 462 (2006) 2457-2479
24. Schmid P.J., and Henningson D.S. Stability and Transition in Shear Flows (2001), Springer
25. Hollerbach R. A spectral solution of the magneto-convection equations in spherical geometry. Int. J. Numer. Meth. Fluids 32 (2000) 773-797
26. Abramowitz M., and Stegun I.A. Handbook of Mathematical Functions (1972), Dover
27. Fox L., and Parker I.B. Chebyshev Polynomials in Numerical Analysis (1968), Oxford University Press, London
28. Hinch E.J. Perturbation Methods (1991), CUP
29. Press W.H., Teukolsky S.A., Vetterling W.T., and Flannery B.P. Numerical Recipies in Fortran 77. second ed. (1992), CUP