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math.NA2026
Accelerated Nehari manifold optimization methods for computing ground state solutions of coupled elliptic systems
Zhaoxing Chen, Wei Liu, Ziqing Xie +1
This paper presents a class of efficient algorithms for computing the ground state solutions of a semilinear elliptic system, which are unstable saddle points of the variational fu…
math.NA2024
Nehari manifold optimization and its application for finding unstable solutions of semilinear elliptic PDEs
Zhaoxing Chen, Wei Liu, Ziqing Xie +1
A Nehari manifold optimization method (NMOM) is introduced for finding 1-saddles, i.e., saddle points with the Morse index equal to one, of a generic nonlinear functional in Hilber…
math.NA2024★ 1 cited
Second-order flows for approaching stationary points of a class of non-convex energies via convex-splitting schemes
Haifan Chen, Guozhi Dong, José A. Iglesias +2
This paper contributes to the exploration of a recently introduced computational paradigm known as second-order flows, which are characterized by novel dissipative hyperbolic parti…