Error Control for Simulations of a Dissociative Quantum System

Katharina Kormann () and Anna Nissen ()
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Katharina Kormann: Uppsala University, Division of Scientific Computing, Department of Information Technology
Anna Nissen: Uppsala University, Division of Scientific Computing, Department of Information Technology

A chapter in Numerical Mathematics and Advanced Applications 2009, 2010, pp 523-531 from Springer

Abstract: 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.

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-11795-4_56

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DOI: 10.1007/978-3-642-11795-4_56

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