25 citations · 51 across the 9 of their papers we have counts for
9 papers
Convergence analysis of a spectral-Galerkin-type search extension method for finding multiple solutions to semilinear problems
Wei Liu, Ziqing Xie, Yongjun Yuan
In this paper, we develop an efficient spectral-Galerkin-type search extension method (SGSEM) for finding multiple solutions to semilinear elliptic boundary value problems. This me…
A constrained gentlest ascent dynamics and its applications to finding excited states of Bose-Einstein condensates
Wei Liu, Ziqing Xie, Yongjun Yuan
In this paper, the gentlest ascent dynamics (GAD) developed in [W. E and X. Zhou, Nonlinearity, 24 (2011), pp. 1831--1842] is extended to a constrained gentlest ascent dynamics (CG…
Second-order flows for computing the ground states of rotating Bose-Einstein condensates
Haifan Chen, Guozhi Dong, Wei Liu +1
Second-order flows in this paper refer to some artificial evolutionary differential equations involving second-order time derivatives distinguished from gradient flows which are co…
Nonmonotone local minimax methods for finding multiple saddle points
Wei Liu, Ziqing Xie, Wenfan Yi
In this paper, by designing a normalized nonmonotone search strategy with the Barzilai--Borwein-type step-size, a novel local minimax method (LMM), which is a globally convergent i…
Normalized Wolfe-Powell-type local minimax method for finding multiple unstable solutions of nonlinear elliptic PDEs
Wei Liu, Ziqing Xie, Wenfan Yi
The local minimax method (LMM) proposed in [Y. Li and J. Zhou, SIAM J. Sci. Comput., 23(3), 840--865 (2001)] and [Y. Li and J. Zhou, SIAM J. Sci. Comput., 24(3), 865--885 (2002)] i…
An Efficient Iterative Method for Solving Multiple Scattering in Locally Inhomogeneous Media
Ziqing Xie, Rui Zhang, Bo Wang +1
In this paper, an efficient iterative method is proposed for solving multiple scattering problem in locally inhomogeneous media. The key idea is to enclose the inhomogeneity of the…
Calculation of SPH and VSH Expansions
Bo Wang, Li-Lian Wang, Ziqing Xie
We present in this paper a spectrally accurate numerical method for computing the spherical/vector spherical harmonic expansion of a function/vector field with given (elemental) no…
Sharp error bounds for Jacobi expansions and Gengenbauer-Gauss quadrature of analytic functions
Xiaodan Zhao, Li-Lian Wang, Ziqing Xie
This paper provides a rigorous and delicate analysis for exponential decay of Jacobi polynomial expansions of analytic functions associated with the Bernstein ellipse. Using an arg…
On Exponential Convergence of Gegenbauer Interpolation and Spectral Differentiation
Ziqing Xie, Li-Lian Wang, Xiaodan Zhao
This paper is devoted to a rigorous analysis of exponential convergence of polynomial interpolation and spectral differentiation based on the Gegenbauer-Gauss and Gegenbauer-Gauss-…