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DOE OSTI · 21432453

A parallel algorithm for solving the 3d Schroedinger equation

Strickland, Michael·Yager-Elorriaga, David
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Abstract

We describe a parallel algorithm for solving the time-independent 3d Schroedinger equation using the finite difference time domain (FDTD) method. We introduce an optimized parallelization scheme that reduces communication overhead between computational nodes. We demonstrate that the compute time, t, scales inversely with the number of computational nodes as t {proportional_to} (N{sub nodes}){sup -0.95} {sup {+-} 0.04}. This makes it possible to solve the 3d Schroedinger equation on extremely large spatial lattices using a small computing cluster. In addition, we present a new method for precisely determining the energy eigenvalues and wavefunctions of quantum states based on a symmetry constraint on the FDTD initial condition. Finally, we discuss the usage of multi-resolution techniques in order to speed up convergence on extremely large lattices.

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71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS97 MATHEMATICS AND COMPUTINGALGORITHMSCOMMUNICATIONSDIFFERENTIAL EQUATIONSEIGENVALUESEQUATIONSFUNCTIONSMATHEMATICAL LOGICMECHANICSPARTIAL DIFFERENTIAL EQUATIONSQUANTUM MECHANICSSCHROEDINGER EQUATIONWAVE EQUATIONSWAVE FUNCTIONS

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Strickland, Michael, Yager-Elorriaga, David. 2010-08-20. A parallel algorithm for solving the 3d Schroedinger equation. https://doi.org/10.1016/j.jcp.2010.04.032

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