5 papers
Numerical analysis of spatiotemporal high-index saddle dynamics for finding multiple solutions of semilinear elliptic problems
Lei Zhang, Xiangcheng Zheng, Shangqin Zhu
This paper presents a rigorous numerical framework for computing multiple solutions of semilinear elliptic problems by spatiotemporal high-index saddle dynamics (HiSD), which exten…
Constructing control landscape for non-convex optimal control of elliptic equation by PDE-constrained high-index saddle dynamics
Ning Du, Yanlin Liu, Lei Zhang +1
Non-convex optimal control arises from various applications but may contain multiple stationary points. Classical solvers usually perform a ``local'' search near a saddle point or…
Numerical analysis for saddle dynamics of some semilinear elliptic problems
Lei Zhang, Xiangcheng Zheng, Shangqin Zhu
This work presents a numerical analysis of computing transition states of semilinear elliptic partial differential equations (PDEs) via the index-1 saddle dynamics, or equivalently…
Nullspace-preserving high-index saddle dynamics method for degenerate multiple solution problems
Kai Jiang, Lei Zhang, Xiangcheng Zheng +1
We propose the nullspace-preserving high-index saddle dynamics (NPHiSD) method for degenerating multiple solution systems in constrained and unconstrained settings. The NPHiSD effi…
Improved high-index saddle dynamics for finding saddle points and solution landscape
Hua Su, Haoran Wang, Lei Zhang +2
We present an improved high-index saddle dynamics (iHiSD) for finding saddle points and constructing solution landscapes, which is a crossover dynamics from gradient flow to tradit…