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Solving Large-Scale Interior Eigenvalue Problems to Investigate the Vibrational Properties of the Boson Peak Regime in Amorphous Materials

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High Performance Computing in Science and Engineering (HPCSE 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12456))

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Abstract

Amorphous solids, like metallic glasses, exhibit an excess of low frequency vibrational states reflecting the break-up of sound due to the strong structural disorder inherent to these materials. Referred to as the boson peak regime of frequencies, how the corresponding eigenmodes relate to the underlying atomic-scale disorder remains an active research topic. In this paper we investigate the use of a polynomial filtered eigensolver for the computation and study of low frequency eigenmodes of a Hessian matrix located in a specific interval close to the boson peak regime. A distributed-memory parallel implementation of a polynomial filtered eigensolver is presented. Our implementation, based on the Trilinos framework, is then applied to a Hessian matrix of an atomistic bulk metallic glass structure derived from a molecular dynamics simulation for the computation of eigenmodes close to the boson peak. In addition, we study the parallel scalability of our implementation on multicore nodes. Our resulting calculations successfully concur with previous atomistic results, and additionally demonstrate a broad cross-over of boson peak frequencies within which sound is seen to break-up.

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Notes

  1. 1.

    http://www-users.cs.umn.edu/~saad/software/EVSL/.

  2. 2.

    https://trilinos.org/packages/.

  3. 3.

    https://portal.hdfgroup.org/.

  4. 4.

    https://math.nist.gov/MatrixMarket/.

  5. 5.

    https://scicomp.ethz.ch/wiki/Euler.

  6. 6.

    https://www.hpcg-benchmark.org/.

  7. 7.

    https://www.cs.virginia.edu/stream/.

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Acknowledgments

The computations have been executed on the Euler compute cluster at ETH Zurich at the expense of a grant of the Seminar for Applied Mathematics. We acknowledge the assistance of the Euler Cluster Support Team.

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Authors and Affiliations

  1. Computer Science Department, ETH Zürich, Zürich, Switzerland

    Giuseppe Accaputo & Peter Arbenz

  2. Condensed Matter Theory Group, Paul Scherrer Institut, Villigen, Switzerland

    Peter M. Derlet

Authors
  1. Giuseppe Accaputo
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  2. Peter M. Derlet
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  3. Peter Arbenz
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Corresponding author

Correspondence to Peter Arbenz .

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Editors and Affiliations

  1. VSB - Technical University of Ostrava, Ostrava-Poruba, Czech Republic

    Tomáš Kozubek

  2. ETH Zurich, Zurich, Switzerland

    Peter Arbenz

  3. Brno University of Technology, Brno, Czech Republic

    Jiří Jaroš

  4. Technical University of Ostrava, Ostrava-Poruba, Czech Republic

    Lubomír Říha

  5. Institute of Mathematics of the CAS, Prague, Czech Republic

    Jakub Šístek

  6. Charles University in Prague, Prague, Czech Republic

    Petr Tichý

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Accaputo, G., Derlet, P.M., Arbenz, P. (2021). Solving Large-Scale Interior Eigenvalue Problems to Investigate the Vibrational Properties of the Boson Peak Regime in Amorphous Materials. In: Kozubek, T., Arbenz, P., Jaroš, J., Říha, L., Šístek, J., Tichý, P. (eds) High Performance Computing in Science and Engineering. HPCSE 2019. Lecture Notes in Computer Science(), vol 12456. Springer, Cham. https://doi.org/10.1007/978-3-030-67077-1_5

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  • DOI: https://doi.org/10.1007/978-3-030-67077-1_5

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