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Hierarchical Matrices in Computations of Electron Dynamics

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Abstract

We discuss the approximation of the meanfield terms appearing in computations of the multi-configuration time-dependent Hartree–Fock method for the solution of the time-dependent multi-particle (electronic) Schrödinger equation by hierarchical matrices. We give theoretical error bounds for the cross approximation defined by low rank approximations of admissible matrix sub-blocks, and illustrate the gain in performance by numerical experiments.

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Authors and Affiliations

  1. Institute for Analysis and Scientific Computing (E101), Vienna University of Technology, Wiedner Hauptstraße 8–10, 1040, Vienna, Austria

    Othmar Koch

  2. Photonics Institute (E387), Vienna University of Technology, Gußhausstraße 27, 1040, Vienna, Austria

    Christopher Ede, Gerald Jordan & Armin Scrinzi

Authors
  1. Othmar Koch
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  2. Christopher Ede
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  3. Gerald Jordan
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  4. Armin Scrinzi
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Correspondence to Othmar Koch.

Additional information

This work was supported by the Austrian Academy of Sciences, APART program.

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Koch, O., Ede, C., Jordan, G. et al. Hierarchical Matrices in Computations of Electron Dynamics. J Sci Comput 42, 447–455 (2010). https://doi.org/10.1007/s10915-009-9330-0

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  • DOI: https://doi.org/10.1007/s10915-009-9330-0

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