@Article{CiCP-25-871,
author = {Yunfeng Xiong and Sihong Shao},
title = {The Wigner Branching Random Walk: Efficient Implementation and Performance Evaluation},
journal = {Communications in Computational Physics},
year = {2018},
volume = {25},
number = {3},
pages = {871--910},
abstract = {<p style="text-align: justify;">To implement the Wigner branching random walk, the particle carrying a
signed weight, either −1 or +1, is more friendly to data storage and arithmetic manipulations
than that taking a real-valued weight continuously from −1 to +1. The
former is called a signed particle and the latter a weighted particle. In this paper, we
propose two efficient strategies to realize the signed-particle implementation. One is
to interpret the multiplicative functional as the probability to generate pairs of particles
instead of the incremental weight, and the other is to utilize a bootstrap filter to
adjust the skewness of particle weights. Performance evaluations on the Gaussian barrier
scattering (2D) and a Helium-like system (4D) demonstrate the feasibility of both
strategies and the variance reduction property of the second approach. We provide an
improvement of the first signed-particle implementation that partially alleviates the
restriction on the time step and perform a thorough theoretical and numerical comparison
among all the existing signed-particle implementations. Details on implementing
the importance sampling according to the quasi-probability density and an efficient
resampling or particle reduction are also provided.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2018-0141},
url = {http://global-sci.org/intro/article_detail/cicp/12832.html}
}