Volume 25, Issue 3
The Wigner Branching Random Walk: Efficient Implementation and Performance Evaluation

Yunfeng Xiong and Sihong Shao

10.4208/cicp.OA-2018-0141

Commun. Comput. Phys., 25 (2019), pp. 871-910.

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  • Abstract

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.

  • History

Published online: 2018-11

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