Semi‐implicit method of high‐index saddle dynamics and application to construct solution landscape
Yue Luo,
Lei Zhang,
Pingwen Zhang
et al.
Abstract: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 co… Show more
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