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Wirth, A.

An extension of spectral methods to quasi-periodic and multiscale problems. (English) Zbl 0874.65075

J. Comput. Phys. 132, No. 2, 285-290 (1997).
An extension of spectral methods to quasi-periodic and multiscale problems is given. It is proposed to change the number of space dimensions which is then multiplied by the number of different scales occuring in the problem. In the higher-dimensional space the problem is a standard periodic problem. The method is validated using the Burgers equation and the two-dimensional linearized Navier-Stokes equation. It is compared with standard spectral or pseudo-spectral methods. The gain in storage and CPU resources is typically proportional to the ratio of scales.
Reviewer: W.Heinrichs (Essen)

Cited in 3 Documents

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
35Q30 Navier-Stokes equations

Keywords:

spectral methods; Burgers equation; Navier-Stokes equation; quasi-periodic problems; multiscale problems
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References:

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