Abstract
We consider in this chapter several multi-dimensional problems, which (a) are of current interest; (b) are suitable for spectral approximations; and (c) can be efficiently solved by using the basic spectral algorithms developed in previous chapters. These include steady state problems: the Helmholtz equation for acoustic scattering and the Stokes equations, as well as time-dependent problems including the Allen-Cahn equation, the Cahn–Hilliard equation, the Navier–Stokes equations, and the Gross–Pitaevskii equation. For applications of spectral methods to other multidimensional problems in science and engineering, we refer, for instance, to Boyd (2001), Canuto et al. (2006), Hesthaven et al. (2007) and the references therein.
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© 2011 Springer Berlin Heidelberg
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Shen, J., Tang, T., Wang, LL. (2011). Applications in Multi-Dimensional Domains. In: Spectral Methods. Springer Series in Computational Mathematics, vol 41. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71041-7_9
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DOI: https://doi.org/10.1007/978-3-540-71041-7_9
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Online ISBN: 978-3-540-71041-7
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