2 citations · 4 across the 10 of their papers we have counts for
10 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…
A Derivative-Free Saddle-search Algorithm With Linear Convergence Rate
Qiang Du, Baoming Shi, Lei Zhang +1
We propose a derivative-free saddle-search algorithm designed to locate transition states using only function evaluations. The algorithm employs a nested architecture consisting of…
Non-convex optimal control governed by nonlinear elliptic partial differential equation: Analysis, functional-based algorithm and control landscape
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 and therefore rely on good…
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…
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…
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…
Convergence analysis of time-splitting projection method for nonlinear quasiperiodic Schrödinger equation
Kai Jiang, Shifeng Li, Xiangcheng Zheng
This work proposes and analyzes an efficient numerical method for solving the nonlinear Schrödinger equation with quasiperiodic potential, where the projection method is applied in…
Understanding high-index saddle dynamics via numerical analysis
Lei Zhang, Pingwen Zhang, Xiangcheng Zheng
High-index saddle dynamics (HiSD) serves as a competitive instrument in searching the any-index saddle points and constructing the solution landscape of complex systems. The Lagran…
Accelerated high-index saddle dynamics method for searching high-index saddle points
Yue Luo, Xiangcheng Zheng, Lei Zhang
The high-index saddle dynamics (HiSD) method [J. Yin, L. Zhang, and P. Zhang, {\it SIAM J. Sci. Comput., }41 (2019), pp.A3576-A3595] serves as an efficient tool for computing index…
Semi-implicit method of high-index saddle dynamics and application to construct solution landscape
Yue Luo, Lei Zhang, Pingwen Zhang +2
We analyze the semi-implicit scheme of high-index saddle dynamics, which provides a powerful numerical method for finding the any-index saddle points and constructing the solution…