Searching the solution landscape by generalized high-index saddle dynamics
| العنوان: | Searching the solution landscape by generalized high-index saddle dynamics |
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| المؤلفون: | Bing Yu, Lei Zhang, Jianyuan Yin |
| المصدر: | Science China Mathematics. 64:1801-1816 |
| بيانات النشر: | Springer Science and Business Media LLC, 2020. |
| سنة النشر: | 2020 |
| مصطلحات موضوعية: | Dynamical systems theory, Field (physics), General Mathematics, Phase (waves), Dynamical Systems (math.DS), 010103 numerical & computational mathematics, 01 natural sciences, Stationary point, Search algorithm, Saddle point, 0103 physical sciences, FOS: Mathematics, Applied mathematics, Mathematics - Dynamical Systems, 0101 mathematics, 010306 general physics, Saddle, Linear stability, Mathematics |
| الوصف: | 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-$k$ 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. |
| تدمد: | 1869-1862 1674-7283 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e3f1a82c566dfb546756feaa2ae1ae0f https://doi.org/10.1007/s11425-020-1737-1 |
| حقوق: | OPEN |
| رقم الأكسشن: | edsair.doi.dedup.....e3f1a82c566dfb546756feaa2ae1ae0f |
| قاعدة البيانات: | OpenAIRE |
Find this article in full text from Springer Verlag. | تدمد: | 18691862 16747283 |
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