A Multidomain Spectral Method for Scalar and Vectorial Poisson Equations with Noncompact Sources

✍ Scribed by P. Grandclément; S. Bonazzola; E. Gourgoulhon; J.-A. Marck

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 178 KB
• Volume: 170
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.2001.6734

✦ Synopsis

We present a spectral method for solving elliptic equations which arise in general relativity, namely three-dimensional scalar Poisson equations, as well as generalized vectorial Poisson equations of the type N + λ ∇( ∇ • N) = S with λ = -1. The source can extend in all the Euclidean space R 3 , provided it decays at least as r -3 . A multidomain approach is used, along with spherical coordinates (r , θ, φ). In each domain, Chebyshev polynomials (in r or 1/r) and spherical harmonics (in θ and φ) expansions are used. If the source decays as r -k the error of the numerical solution is shown to decrease at least as N -2(k-2) , where N is the number of Chebyshev coefficients. The error is even evanescents; i.e., it decreases as exp(-N ), if the source does not contain any spherical harmonics of index l ≥ k -3 (scalar case) or l ≥ k -5 (vectorial case).