Error Estimate of a Quasi-Monte Carlo Time-Splitting Pseudospectral Method for Nonlinear Schrödinger Equation with Random Potentials

IF 2.1 3区工程技术 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2024-01-30 DOI:10.1137/22m1525181

Zhizhang Wu, Zhiwen Zhang, Xiaofei Zhao

引用次数: 0

Abstract

SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 1, Page 1-29, March 2024.
Abstract. In this paper, we consider the numerical solution of a nonlinear Schrödinger equation with spatial random potential. The randomly shifted quasi-Monte Carlo (QMC) lattice rule combined with the time-splitting pseudospectral discretization is applied and analyzed. The nonlinearity in the equation induces difficulties in estimating the regularity of the solution in random space. By the technique of weighted Sobolev space, we identify the possible weights and show the existence of QMC that converges optimally at the almost-linear rate without dependence on dimensions. The full error estimate of the scheme is established. We present numerical results to verify the accuracy and investigate the wave propagation.

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带随机势能的非线性薛定谔方程准蒙特卡洛时间分割伪谱法的误差估计

SIAM/ASA 不确定性量化期刊》，第 12 卷，第 1 期，第 1-29 页，2024 年 3 月。摘要本文考虑了具有空间随机势的非线性薛定谔方程的数值求解。应用随机移动准蒙特卡罗（QMC）晶格规则结合时间分割伪谱离散化进行了分析。方程的非线性给估计随机空间解的正则性带来了困难。通过加权索波列夫空间技术，我们确定了可能的权重，并证明了 QMC 的存在，它以几乎线性的速度最佳收敛，且不依赖于维数。我们建立了该方案的全误差估计。我们给出了数值结果来验证其准确性，并研究了波的传播。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Siam-Asa Journal on Uncertainty Quantification Mathematics-Statistics and Probability

CiteScore

3.70

自引率

0.00%

发文量

期刊介绍： SIAM/ASA Journal on Uncertainty Quantification (JUQ) publishes research articles presenting significant mathematical, statistical, algorithmic, and application advances in uncertainty quantification, defined as the interface of complex modeling of processes and data, especially characterizations of the uncertainties inherent in the use of such models. The journal also focuses on related fields such as sensitivity analysis, model validation, model calibration, data assimilation, and code verification. The journal also solicits papers describing new ideas that could lead to significant progress in methodology for uncertainty quantification as well as review articles on particular aspects. The journal is dedicated to nurturing synergistic interactions between the mathematical, statistical, computational, and applications communities involved in uncertainty quantification and related areas. JUQ is jointly offered by SIAM and the American Statistical Association.