Searching the solution landscape by generalized high-index saddle dynamics
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Publication:2238496
DOI10.1007/S11425-020-1737-1zbMATH Open1482.37086arXiv2002.10690OpenAlexW3008343542MaRDI QIDQ2238496
Author name not available (Why is that?)
Publication date: 1 November 2021
Published in: (Search for Journal in Brave)
Abstract: We introduce a generalized numerical algorithm to construct the solution landscape, which is a pathway map consisting of all stationary points and their connections. Based on the high-index optimization-based shrinking dimer (HiOSD) method for gradient systems, a generalized high-index saddle dynamics (GHiSD) is proposed to compute any-index saddles of dynamical systems. Linear stability of the index- saddle point can be proved for the GHiSD system. A combination of the downward search algorithm and the upward search algorithm is applied to systematically construct the solution landscape, which not only provides a powerful and efficient way to compute multiple solutions without tuning initial guesses, but also reveals the relationships between different solutions. Numerical examples, including a three-dimensional example and the phase field model, demonstrate the novel concept of the solution landscape by showing the connected pathway maps.
Full work available at URL: https://arxiv.org/abs/2002.10690
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