Skip to main content
SpringerLink
Log in

Parallel Numerical Calculations of Quantum Trimer Systems

  • Conference paper
Mathematical Modeling and Computational Science (MMCP 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7125))

Abstract

In this report, total angular momentum representation is used in order to write the Schrödinger equation for the trimer as a finite system of coupled three-dimensional differential equations. The complex scaling method is used for studying resonances of trimers. To get a numerical approximation of the problem, a combination of the high-order finite element method with the spectral method is used. This approach results in a generalized eigenvalue problem. Its spectrum describes bound states and resonances of the trimers. Different parallelization techniques (OpenMP, MPI, GPGPU) are considered for the calculation of the matrix elements of the problem. Their efficiency and scalability are discussed and compared.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Balslev, E., Combes, J.M.: Spectral properties of many-body Schrödinger operators with dilatation-analytic interactions. Commun. Math. Phys. 22, 280–294 (1971)

    Article  MATH  Google Scholar 

  2. CUDA BLAS library documentation, http://www.nvidia.com/cuda

  3. Fedorov, D.V., Jensen, A.S.: The Three-Body Continuum Coulomb Problem and the 3α Structure of 12C. Phys. Lett. B 389, 631–636 (1996)

    Article  Google Scholar 

  4. Gagin, A., Yarevsky, E., Salci, M., Elander, N.: Eigen Energies and the Statistical Distributions of the Rovibrational Levels of the Bosonic van der Waals Argon Trimer. J. Phys. Chem. A 113, 14979–14986 (2009)

    Article  Google Scholar 

  5. Saad, Y.: Numerical Methods for Large Eigenvalue Problems. Halstead Press (1992)

    Google Scholar 

  6. Zienkiewicz, O.C., Taylor, R.L.: The finite element method. The basis, vol. 1. Butterworth-Heinemann (2000)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computational Physics, St. Petersburg State University, RU-198504, St Petersburg, Russia

    Evgeny Yarevsky

Authors
  1. Evgeny Yarevsky
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Laboratory of Information Technologies, Joint Institute for Nuclear Research, 6 Joliot Curie St., 141980, Dubna, Russia

    Gheorghe Adam

  2. Technical University of Košice, Němcovej 32, 042 00, Košice, Slovakia

    Ján Buša

  3. Pavol Jozef Šafárik University, Jesenná 5, 040 01, Košice, Slovakia

    Michal Hnatič

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Yarevsky, E. (2012). Parallel Numerical Calculations of Quantum Trimer Systems. In: Adam, G., Buša, J., Hnatič, M. (eds) Mathematical Modeling and Computational Science. MMCP 2011. Lecture Notes in Computer Science, vol 7125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28212-6_35

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-28212-6_35

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28211-9

  • Online ISBN: 978-3-642-28212-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation