Communication-Efficient Algorithms for Numerical Quantum Dynamics

  • Magnus Gustafsson
  • Katharina Kormann
  • Sverker Holmgren
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7134)


The time-dependent Schrödinger equation (TDSE) describes the quantum dynamical nature of molecular processes. However, numerical simulations of this linear, high-dimensional partial differential equation (PDE) rapidly become computationally very demanding and massive-scale parallel computing is needed to tackle many interesting problems. We present recent improvements to our MPI and OpenMP parallelized code framework HAParaNDA for solving high-dimensional PDE problems like the TDSE. By using communication-efficient high-order finite difference methods and Lanczos time propagators, we are able to accurately and efficiently solve TDSE problems in up to five dimensions on medium-sized clusters. We report numerical experiments which show that the solver scales well up to at least 4096 computing cores, also on computer systems with commodity communication networks.


Lanczos algorithm high-order finite difference parallel scalability 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Magnus Gustafsson
    • 1
  • Katharina Kormann
    • 1
  • Sverker Holmgren
    • 1
  1. 1.Division of Scientific ComputingUppsala UniversityUppsalaSweden

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