Fourier transform on sparse grids: Code design and the time dependent Schr�dinger equation

Gradinaru, V.
May 2007
Computing;May2007, Vol. 80 Issue 1, p1
Academic Journal
The pseudo-spectral method together with a Strang-splitting are well suited for the discretization of the time-dependent Schr�dinger equation with smooth potential. The curse of dimensionality limits this approach to low dimensions, if we stick to full grids. Theoretically, sparse grids allow accurate computations in (moderately) higher dimensions, provided that we supply an efficient Fourier transform. Motivated by this application, the design of the Fourier transform on sparse grids in multiple dimensions is described in detail. The focus of this presentation is on issues of flexible implementation and numerical studies of the convergence.


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