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math.NA2025
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…
math.NA2025
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…
math.NA2025★ 1 cited
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…