A model-free shrinking-dimer saddle dynamics for finding saddle point and solution landscape

Zhang, Lei; Zhang, Pingwen; Zheng, Xiangcheng

doi:10.1007/s13160-023-00604-8

Japan J. Indust. Appl. Math.

2023

DOI: 10.1007/s13160-023-00604-8

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A model-free shrinking-dimer saddle dynamics for finding saddle point and solution landscape

Lei Zhang

Pingwen Zhang

Xiangcheng Zheng

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2024

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Cited by 2 publications

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Semi‐implicit method of high‐index saddle dynamics and application to construct solution landscape

Luo,

Zhang,

Zhang

et al. 2024

Numerical Methods Partial

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We analyze the semi‐implicit scheme of high‐index saddle dynamics, which provides a powerful numerical method for finding the any‐index saddle points and constructing the solution landscape. Compared with the explicit schemes of saddle dynamics, the semi‐implicit discretization relaxes the step size and accelerates the convergence, but the corresponding numerical analysis encounters new difficulties compared to the explicit scheme. Specifically, the orthonormal property of the eigenvectors at each time step could not be fully employed due to the semi‐implicit treatment, and computations of the eigenvectors are coupled with the orthonormalization procedure, which further complicates the numerical analysis. We address these issues to prove error estimates of the semi‐implicit scheme via, for example, technical splittings and multi‐variable circulating induction procedure. We further analyze the convergence rate of the generalized minimum residual solver for solving the semi‐implicit system. Extensive numerical experiments are carried out to substantiate the efficiency and accuracy of the semi‐implicit scheme in constructing solution landscapes of complex systems.

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Semi‐implicit method of high‐index saddle dynamics and application to construct solution landscape

Luo,

Zhang,

Zhang

et al. 2024

Numerical Methods Partial

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Multistability for Nematic Liquid Crystals in Cuboids with Degenerate Planar Boundary Conditions

Shi,

Han,

Majumdar

et al. 2024

SIAM J. Appl. Math.

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A model-free shrinking-dimer saddle dynamics for finding saddle point and solution landscape

Cited by 2 publications

References 53 publications

Semi‐implicit method of high‐index saddle dynamics and application to construct solution landscape

Semi‐implicit method of high‐index saddle dynamics and application to construct solution landscape

Multistability for Nematic Liquid Crystals in Cuboids with Degenerate Planar Boundary Conditions

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