A Parallel Algorithm for Solving the 3d Schrodinger Equation

Details A Parallel Algorithm for Solving the 3d Schrodinger Equation A Parallel Algorithm for Solving the 3d Schrodinger Equation

2009-04-06

arxiv.org/abs/0904.0939v4

J.Comp.Phys.229:6015-6026,2010

Physics

Quantum Physics

18 pages, 7 figures; published version

Scientific paper

10.1016/j.jcp.2010.04.032

We describe a parallel algorithm for solving the time-independent 3d Schrodinger 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 ~ N_nodes^(-0.95 +/- 0.04). This makes it possible to solve the 3d Schrodinger 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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