Accuracy studies of a parallel algorithm for solving the hydrodynamic formulation of the time-dependent Schrodinger equation

摘要

This work examines the accuracy of a parallel moving least squares algorithm for solving the governing equations of the hydrodynamic formulation of quantum mechanics. The algorithm solves the associated linear least squares problems using either normal equations or QR factorization. The accuracy of the algorithm is studied for both the free particle and the harmonic oscillator, and the results of a series of experiments designed to determine the spatial and temporal dependence of the accuracies are presented. In closing, a few qualitative observations concerning the performance of the algorithm are offered for consideration.