A new method for fast transforms in parity-mixed PDEs: Part I. Numerical techniques and analysis

  • Authors:

  • Geoffrey M. Vasil;Nicholas H. Brummell;Keith Julien

  • Affiliations:

  • Department of Atmospheric and Oceanic Sciences and JILA, University of Colorado, Boulder, CO 80309, United States;Department of Astrophysical and Planetary Sciences and JILA, University of Colorado, Boulder, CO 80309, United States and Department of Applied Mathematics, University of California, Santa Cruz, C ...;Department of Applied Mathematics, University of Colorado, Boulder, CO 80309, United States

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2008

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Abstract

We address the problem of parity mixing, where the projection of a variable expressed as a finite series of half-period cosine (sine) functions onto a half-period sine (cosine) function basis is not finite. We propose new fast methods for computing these complicated projections exactly up to some arbitrary degree using fast Fourier transforms. This method has immediate applications for pseudospectral solutions of many systems of partial differential equations.