2020/11/26 by Jianyuan Yin, Zhen Huang, Yin, Jianyuan +3 · 5 citations
Earth and Planetary Sciences · Environmental Science · #Meteorological Phenomena and Simulations #Climate variability and models #Arctic and Antarctic ice dynamics
paper · doi:10.48550/arxiv.2011.13173
We propose a constrained high-index saddle dynamics (CHiSD) method to search for index-k saddle points of an energy functional subject to equality constraints. With Riemannian manifold tools, the CHiSD is derived in a minimax framework, and its linear stability at an index-k saddle point is proved. To ensure the manifold property, the CHiSD is numerically implemented using retractions and vector transport. Then we present a numerical approach by combining CHiSD with downward and upward search algorithms to construct the solution landscape in the presence of equality constraints. We apply the Thomson problem and the Bose-Einstein condensation as numerical examples to demonstrate the efficiency of the proposed method.