Gross-Pitaevskii方程和特征向量非线性：数值方法和算法

IF 10.8 1区数学 Q1 MATHEMATICS, APPLIED

SIAM Review Pub Date : 2025-05-08 DOI:10.1137/22m1516324

Patrick Henning, Elias Jarlebring

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引用次数: 0

摘要

SIAM评论，第67卷，第2期，第256-317页，2025年5月。摘要。本文对Gross-Pitaevskii特征值问题（GPEVP）的数值方法进行了综述。GPEVP是量子物理中描述超冷玻色子气体基态的重要非线性Schrödinger方程。GPEVP的离散化导致了一个具有特征向量非线性的非线性特征值问题。在处理GPEVP的文献中，丰富多样的数值技术有线性代数、偏微分方程、数值优化以及黎曼流形上的梯度流的成分。我们回顾了这些异质的文献，重点是对看似不同的方法、算法和方法属性的统一处理，并指出了该领域存在的问题和未来的挑战。

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The Gross–Pitaevskii Equation and Eigenvector Nonlinearities: Numerical Methods and Algorithms

SIAM Review, Volume 67, Issue 2, Page 256-317, May 2025.
Abstract.In this review paper, we provide an overview of numerical methods used in the study of the Gross–Pitaevskii eigenvalue problem (GPEVP). The GPEVP is an important nonlinear Schrödinger equation that is used in quantum physics to describe the ground states of ultracold bosonic gases. The discretization of the GPEVP leads to a nonlinear eigenvalue problem with eigenvector nonlinearities. The rich variety of numerical techniques in the literature for tackling the GPEVP has ingredients from linear algebra, partial differential equations, and numerical optimization as well as gradient flows on Riemannian manifolds. We review this heterogeneous body of literature with a focus on a unified treatment of seemingly different approaches, algorithms, and method properties, and we point to open problems and future challenges in the field.

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来源期刊

SIAM Review 数学-应用数学

CiteScore

16.90

自引率

0.00%

发文量

期刊介绍： Survey and Review feature papers that provide an integrative and current viewpoint on important topics in applied or computational mathematics and scientific computing. These papers aim to offer a comprehensive perspective on the subject matter. Research Spotlights publish concise research papers in applied and computational mathematics that are of interest to a wide range of readers in SIAM Review. The papers in this section present innovative ideas that are clearly explained and motivated. They stand out from regular publications in specific SIAM journals due to their accessibility and potential for widespread and long-lasting influence.