A Package for Modeling Geophysical ProcessesSPHEREPACK 3.2 is a collection of FORTRAN77 programs and subroutines facilitating computer modeling of geophysical processes. The package contains subroutines for computing common differential operators including divergence, vorticity, latitudinal derivatives, gradients, the Laplacian of both scalar and vector functions, and the inverses of these operators. For example, given divergence and vorticity, the package can be used to compute velocity components, then the Laplacian inverse can be used to solve the scalar and vector Poisson equations. The package also contains routines for computing the associated Legendre functions, Gauss points and weights, multiple fast Fourier transforms, and for converting scalar and vector fields between geophysical and mathematical spherical coordinates.Example programs are provided for solving these equations on the full sphere: advection, Helmholz, shallow-waterEach program serves two purposes: as a template to guide you in writing your own codes utilizing the SPHEREPACK routines, and as a demonstration on your computer that you can correctly produce SPHEREPACK executables.

References in zbMATH (referenced in 26 articles )

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  1. Bryngelson, Spencer H.; Freund, Jonathan B.: Floquet stability analysis of capsules in viscous shear flow (2018)
  2. Montanelli, Hadrien; Nakatsukasa, Yuji: Fourth-order time-stepping for stiff PDEs on the sphere (2018)
  3. Andrew Dawson: Windspharm: A High-Level Library for Global Wind Field Computations Using Spherical Harmonics (2016) not zbMATH
  4. Townsend, Alex; Wilber, Heather; Wright, Grady B.: Computing with functions in spherical and polar geometries. I. The sphere (2016)
  5. Liang, Qin; Jiang, Kai; Zhang, Pingwen: Efficient numerical schemes for solving the self-consistent field equations of flexible-semiflexible diblock copolymers (2015)
  6. Tiwari, Arpit; Freund, Jonathan B.; Pantano, Carlos: A diffuse interface model with immiscibility preservation (2013)
  7. Ehrendorfer, Martin: Spectral numerical weather prediction models. (2012)
  8. Lau, Stephen R.; Price, Richard H.: Sparse spectral-tau method for the three-dimensional helically reduced wave equation on two-center domains (2012)
  9. Zhao, Hong; Shaqfeh, Eric S. G.: The dynamics of a vesicle in simple shear flow (2011)
  10. Tygert, Mark: Fast algorithms for spherical harmonic expansions. III (2010)
  11. Cohen, Michael I.; Pfeiffer, Harald P.; Scheel, Mark A.: Revisiting event horizon finders (2009)
  12. Tygert, Mark: Fast algorithms for spherical harmonic expansions. II. (2008)
  13. Lau, Stephen R.; Price, Richard H.: Multidomain spectral method for the helically reduced wave equation (2007)
  14. Blais, J. A. R.; Provins, D. A.; Soofi, M. A.: Spherical harmonic transforms for discrete multiresolution applications (2006) ioport
  15. Blais, J. A. R.; Soofi, M. A.: Spherical harmonic transforms using quadratures and least squares (2006)
  16. Rokhlin, Vladimir; Tygert, Mark: Fast algorithms for spherical harmonic expansions (2006)
  17. Szmytkowski, Radosław: Closed form of the generalized Green’s function for the Helmholtz operator on the two-dimensional unit sphere (2006)
  18. Blais, J. A. R.; Provins, D. A.; Soofi, M. A.: Optimization of spherical harmonic transform computations (2005)
  19. Matthews, Paul C.: Pattern formation on a sphere (2004)
  20. Swarztrauber, Paul N.; Spotz, William F.: Spherical harmonic projectors (2004)

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