Hybrid Chebyshev function bases for sparse spectral methods in paritymixed PDEs on an infinite domain
Abstract
We present a numerical spectral method to solve systems of differential equations on an infinite interval y ∈ ( ∞ , ∞) in presence of linear differential operators of the form Q (y)^{(∂ /∂y) b} (where Q (y) is a rational fraction and b a positive integer). Even when these operators are not paritypreserving, we demonstrate how a mixed expansion in interleaved Chebyshev rational functions TB_{n} (y) and SB_{n} (y) preserves the sparsity of their discretization. This paves the way for fast O (Nln N) and spectrally accurate mixed implicitexplicit timemarching of sets of linear and nonlinear equations in unbounded geometries.
 Publication:

Journal of Computational Physics
 Pub Date:
 November 2017
 DOI:
 10.1016/j.jcp.2017.08.034
 arXiv:
 arXiv:1703.07441
 Bibcode:
 2017JCoPh.349..474M
 Keywords:

 Spectral methods;
 Sparse solvers;
 Chebyshev functions;
 Unbounded domain;
 Localized dynamics;
 Physics  Fluid Dynamics;
 Physics  Computational Physics
 EPrint:
 26 pages, 11 figures, submitted for publication