Fourier transform on sparse grids: Code design and the time dependent Schrödinger equation

Authors:
V. Gradinaru
Affiliations:
Universität Tübingen, Auf der Morgenstelle 10, 72076, Tübingen, Germany
Venue:
Computing
Year:
2007

Citing 5
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Abstract

The pseudo-spectral method together with a Strang-splitting are well suited for the discretization of the time-dependent Schrödinger 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.