A parallel algorithm for solving the 3d Schrodinger equation

JOURNAL OF COMPUTATIONAL PHYSICS

卷:229

Article

Strickland, Michael¹  Yager-Elorriaga, David¹ 

[1] Gettysburg Coll, Dept Phys, Gettysburg, PA 17325 USA

关键词: Quantum mechanics;    Schrodinger equations;    Parallelized algorithm;    Finite difference time domain;   

DOI  :  10.1016/j.jcp.2010.04.032

来源: Elsevier

【 摘 要 】

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 proportional to (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. (C) 2010 Elsevier Inc. All rights reserved

【 授权许可】

Free