105 citations · 249 across the 20 of their papers we have counts for
17 papers · 1 filter
Explicit and CPU/GPU parallel energy-preserving schemes for the Klein-Gordon-Schrödinger equations
Xuelong Gu, Yushun Wang, Ziyu Wu +2
A highly efficient energy-preserving scheme for univariate conservative or dissipative systems was recently proposed in [Comput. Methods Appl. Mech. Engrg. 425 (2024) 116938]. This…
A novel high-order linearly implicit and energy-stable additive Runge-Kutta methods for gradient flow models
Xuelong Gu, Wenjun Cai, Yushun Wang
This paper introduces a novel paradigm for constructing linearly implicit and high-order unconditionally energy-stable schemes for general gradient flows, utilizing the scalar auxi…
Energy stable and maximum bound principle preserving schemes for the Allen-Cahn equation based on the Saul'yev methods
Xuelong Gu, Yushun Wang, Wenjun Cai
The energy dissipation law and maximum bound principle are significant characteristics of the Allen-Chan equation. To preserve discrete counterpart of these properties, the linear…
Unconditional convergence of conservative spectral Galerkin methods for the coupled fractional nonlinear Klein-Gordon-Schrödinger equations
Dongdong Hu, Yayun Fu, Wenjun Cai +1
In this work, two novel classes of structure-preserving spectral Galerkin methods are proposed which based on the Crank-Nicolson scheme and the exponential scalar auxiliary variabl…
Linearly implicit energy-preserving integrating factor methods for the 2D nonlinear Schrödinger equation with wave operator and convergence analysis
Xuelong Gu, Wenjun Cai, Chaolong Jiang +1
In this paper, we develop a novel class of linear energy-preserving integrating factor methods for the 2D nonlinear Schrödinger equation with wave operator (NLSW), combining the sc…
Efficient energy-preserving exponential integrators for multi-components Hamiltonian systems
X. Gu, C. Jiang, Y. Wang +1
In this paper, we develop a framework to construct energy-preserving methods for multi-components Hamiltonian systems, combining the exponential integrator and the partitioned aver…
Arbitrary high-order linearly implicit energy-preserving algorithms for Hamiltonian PDEs
Yonghui Bo, Yushun Wang, Wenjun Cai
In this paper, we present a novel strategy to systematically construct linearly implicit energy-preserving schemes with arbitrary order of accuracy for Hamiltonian PDEs. Such novel…
An explicit and practically invariants-preserving method for conservative systems
Wenjun Cai, Yuezheng Gong, Yushun Wang
An explicit numerical strategy that practically preserves invariants is derived for conservative systems by combining an explicit high-order Runge-Kutta (RK) scheme with a simple m…
Two novel classes of arbitrary high-order structure-preserving algorithms for canonical Hamiltonian systems
Yonghui Bo, Wenjun Cai, Yushun Wang
In this paper, we systematically construct two classes of structure-preserving schemes with arbitrary order of accuracy for canonical Hamiltonian systems. The one class is the symp…
A structure-preserving algorithm for the fractional nonlinear Schrödinger equation based on the SAV approach
Yayun Fu, Wenjun Cai, Yushun Wang
The main objective of this paper is to present an efficient structure-preserving scheme, which is based on the idea of the scalar auxiliary variable approach, for solving the space…
A linearly implicit structure-preserving scheme for the fractional sine-Gordon equation based on the IEQ approach
Yayun Fu, Wenjun Cai, Yushun Wang
This paper aims to develop a linearly implicit structure-preserving numerical scheme for the space fractional sine-Gordon equation, which is based on the newly developed invariant…
A linearly implicit energy-preserving exponential integrator for the nonlinear Klein-Gordon equation
Chaolong Jiang, Yushun Wang, Wenjun Cai
In this paper, we generalize the exponential energy-preserving integrator proposed in the recent paper [SIAM J. Sci. Comput. 38(2016) A1876-A1895] for conservative systems, which n…
A linearly implicit structure-preserving scheme for the Camassa-Holm equation based on multiple scalar auxiliary variables approach
Chaolong Jiang, Yuezheng Gong, Wenjun Cai +1
In this paper, we present a linearly implicit energy-preserving scheme for the Camassa-Holm equation by using the multiple scalar auxiliary variables approach, which is first devel…
A novel linearized and momentum-preserving Fourier pseudo-spectral scheme for the Rosenau-Korteweg de Vries equation
Chaolong Jiang, Jin Cui, Wenjun Cai +1
In this paper, we design a novel linearized and momentum-preserving Fourier pseudo-spectral scheme to solve the Rosenau-Korteweg de Vries equation. With the aid of a new semi-norm…
Structure-preserving algorithms for the two-dimensional sine-Gordon equation with Neumann boundary conditions
Wenjun Cai, Chaolong Jiang, Yushun Wang
This paper presents two kinds of strategies to construct structure-preserving algorithms with homogeneous Neumann boundary conditions for the sine-Gordon equation, while most exist…
Partitioned AVF methods
Wenjun Cai, Haochen Li, Yushun Wang
The classic second-order average vector field (AVF) method can exactly preserve the energy for Hamiltonian ordinary differential equations and partial differential equations. Howev…
A Novel Sixth Order Energy-Conserved Method for Three-Dimensional Time-Domain Maxwell's Equations
Chaolong Jiang, Wenjun Cai, Yushun Wang +1
In this paper, a novel sixth order energy-conserved method is proposed for solving the three-dimensional time-domain Maxwell's equations. The new scheme preserves five discrete ene…