Parallel Numerical Calculations of Quantum Trimer Systems

  • Evgeny Yarevsky
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7125)


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.


Quantum trimer spectral method finite element method parallel calculations MPI OpenMP GPGPU 


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  1. 1.
    Balslev, E., Combes, J.M.: Spectral properties of many-body Schrödinger operators with dilatation-analytic interactions. Commun. Math. Phys. 22, 280–294 (1971)CrossRefzbMATHGoogle Scholar
  2. 2.
    CUDA BLAS library documentation,
  3. 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)CrossRefGoogle Scholar
  4. 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)CrossRefGoogle Scholar
  5. 5.
    Saad, Y.: Numerical Methods for Large Eigenvalue Problems. Halstead Press (1992)Google Scholar
  6. 6.
    Zienkiewicz, O.C., Taylor, R.L.: The finite element method. The basis, vol. 1. Butterworth-Heinemann (2000)Google Scholar

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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Evgeny Yarevsky
    • 1
  1. 1.Department of Computational PhysicsSt. Petersburg State UniversitySt PetersburgRussia

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