

Preprint 90/2001
Wavelet approximation of correlated wavefunctions. II. Hyperbolic wavelets and adaptive approximation schemes
Hongjun Luo, Dietmar Kolb, Heinz-Jürgen Flad, Wolfgang Hackbusch, and Thomas Koprucki
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Submission date: 27. Mar. 2002
Pages: 26
published in: The journal of chemical physics, 117 (2002) 8, p. 3625-3638
DOI number (of the published article): 10.1063/1.1494800
Bibtex
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Abstract:
We have studied various aspects concerning the use of hyperbolic wavelets and adaptive approximation schemes for
wavelet expansions of correlated wavefunctions. In order to analyze the consequences of reduced regularity
of the wavefunction at the electron-electron cusp,
we first considered a realistic exactly solvable many-particle model in one dimension.
Convergence rates of wavelet expansions, with respect to and
norms and the energy, were established for this model.
We compare the performance of hyperbolic wavelets and their extensions through adaptive refinement in the cusp region,
to a fully adaptive treatment based on the energy contribution of individual wavelets.
Although hyperbolic wavelets show an inferior convergence behavior, they can be easily refined in the cusp region
yielding an optimal convergence rate for the energy.
Preliminary results for the helium atom are presented, which demonstrate the transferability of our observations
to more realistic systems. We propose a contraction scheme for wavelets in the cusp region, which
reduces the number of degrees of freedom and yields a favorable cost to benefit ratio for the evaluation
of matrix elements.