Time marching multilevel techniques for evolutionary dissipative problems

In this article we use a pseudospectral Fourier discretization in conjuncti on with a multilevel splitting of high and low modes to solve dissipative p artial differential equations. We develop unconditionally stable explicit t echniques for the temporal integration of the linear terms and apply them t o the high modes equation, improving the overall temporal stability of the multilevel method and resulting in a competitive fully explicit numerical s cheme 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 compa ring the resulting method with the standard spectral collocation associated with regular temporal integration schemes.