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Constrained High-index Saddle Dynamics for the Solution Landscape with Equality Constraints by Yin, Jianyuan; Huang, Zhen; Zhang, Lei is a scholarly article available to read on EtoBox.

What is Constrained High-index Saddle Dynamics for the Solution Landscape with Equality Constraints about?

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.

Author

Yin, Jianyuan; Huang, Zhen; Zhang, Lei

Published

2020

Language

EN