Efficient Magnus-type integrators for solar energy conversion in Hubbard models

Journal of Computational Mathematics and Data Science Pub Date : 2022-01-01 DOI:10.1016/j.jcmds.2021.100018

Winfried Auzinger , Juliette Dubois , Karsten Held , Harald Hofstätter , Tobias Jawecki , Anna Kauch , Othmar Koch , Karolina Kropielnicka , Pranav Singh , Clemens Watzenböck

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引用次数: 3

Abstract

Strongly interacting electrons in solids are generically described by Hubbard-type models, and the impact of solar light can be modeled by an additional time-dependence. This yields a finite dimensional system of ordinary differential equations (ODE)s of Schrödinger type, which can be solved numerically by exponential time integrators of Magnus type. The efficiency may be enhanced by combining these with operator splittings. We will discuss several different approaches of employing exponential-based methods in conjunction with an adaptive Lanczos method for the evaluation of matrix exponentials and compare their accuracy and efficiency. For each integrator, we use defect-based local error estimators to enable adaptive time-stepping. This serves to reliably control the approximation error and reduce the computational effort.

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哈伯德模型中太阳能转换的高效magnus型积分器

固体中强相互作用的电子通常用哈伯德模型来描述，太阳光线的影响可以通过额外的时间依赖性来建模。这产生了一个Schrödinger型的有限维常微分方程(ODE)s系统，它可以用Magnus型指数时间积分器进行数值求解。将其与作业者分流相结合，可以提高效率。我们将讨论几种不同的方法，将基于指数的方法与自适应Lanczos方法结合使用，用于矩阵指数的评估，并比较它们的准确性和效率。对于每个积分器，我们使用基于缺陷的局部误差估计器来实现自适应时间步进。这有助于可靠地控制逼近误差，减少计算量。

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

Journal of Computational Mathematics and Data Science

CiteScore

3.00

自引率

0.00%

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