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Error Control for Simulations of a Dissociative Quantum System

In: Numerical Mathematics and Advanced Applications 2009

Author

Listed:
  • Katharina Kormann

    (Uppsala University, Division of Scientific Computing, Department of Information Technology)

  • Anna Nissen

    (Uppsala University, Division of Scientific Computing, Department of Information Technology)

Abstract

We present a framework for solving the Schrödinger equation modeling the interaction of a dissociative quantum system with a laser field. A perfectly matched layer (PML) is used to handle non-reflecting boundaries and the Schrödinger equation is discretized with high-order finite differences in space and an h, p-adaptive Magnus–Arnoldi propagator in time. We use a posteriori error estimation theory to control the global error of the numerical discretization. The parameters of the PML are chosen to meet the same error tolerance. We apply our framework to the IBr molecule, for which numerical experiments show that the total error can be controlled efficiently. Moreover, we provide numerical evidence that the Magnus–Arnoldi solver outperforms the implicit Crank–Nicolson scheme by far.

Suggested Citation

  • Katharina Kormann & Anna Nissen, 2010. "Error Control for Simulations of a Dissociative Quantum System," Springer Books, in: Gunilla Kreiss & Per Lötstedt & Axel Målqvist & Maya Neytcheva (ed.), Numerical Mathematics and Advanced Applications 2009, pages 523-531, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-11795-4_56
    DOI: 10.1007/978-3-642-11795-4_56
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