Time marching multilevel techniques for evolutionary dissipative problems

doi:10.1137/S1064827598339967

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Time marching multilevel techniques for evolutionary dissipative problems

2001-01-01

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DOI：10.1137/S1064827598339967

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Abstract

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In this article we use a pseudospectral Fourier discretization in conjunction with a multilevel splitting of high and low modes to solve dissipative partial differential equations. We develop unconditionally stable explicit techniques for the temporal integration of the linear terms and apply them to the high modes equation, improving the overall temporal stability of the multilevel method and resulting in a competitive fully explicit numerical scheme for nonlinear problems. In the cases where the linear term determines the time step restriction, numerical experiments with the Burgers equation in one and two dimensions showed substantial CPU cost reduction when comparing the resulting method with the standard spectral collocation associated with regular temporal integration schemes.

Keywords:

Runge-Kutta methods

nonlinear Galerkin

Fourier collocation

Burgers equation