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Chaolong Jiang - One of the best experts on this subject based on the ideXlab platform.

  • arbitrarily high order structure preserving schemes for the gross pitaevskii equation with angular momentum rotation
    Computer Physics Communications, 2021
    Co-Authors: Chaolong Jiang, Yushun Wang, Jin Cui
    Abstract:

    Abstract In this paper, we design a novel class of arbitrarily high-order structure-preserving numerical schemes for the time-dependent Gross–Pitaevskii equation with angular momentum rotation. Based on the idea of the scalar auxiliary variable approach which is proposed in the recent papers [J. Comput. Phys., 353 (2018) 407–416 and SIAM Rev., 61(2019) 474–506] for developing Energy stable schemes for gradient flow systems, we firstly reformulate the Gross–Pitaevskii equation into an equivalent system with a modified Energy Conservation Law. The reformulated system is then discretized by the Gauss collocation method in time and the standard Fourier pseudo-spectral method in space, respectively. We show that the proposed schemes can preserve the discrete mass and modified Energy exactly. Numerical results are addressed to verify the efficiency and high-order accuracy of the proposed schemes.

  • a linearly implicit and local Energy preserving scheme for the sine gordon equation based on the invariant Energy quadratization approach
    arXiv: Numerical Analysis, 2018
    Co-Authors: Chaolong Jiang, Wenjun Cai, Yushun Wang
    Abstract:

    In this paper, we develop a novel, linearly implicit and local Energy-preserving scheme for the sine-Gordon equation. The basic idea is from the invariant Energy quadratization approach to construct Energy stable schemes for gradient systems, which are Energy dispassion. We here take the sine-Gordon equation as an example to show that the invariant Energy quadratization approach is also an efficient way to construct linearly implicit and local Energy-conserving schemes for Energy-conserving systems. Utilizing the invariant Energy quadratization approach, the sine-Gordon equation is first reformulated into an equivalent system, which inherits a modified local Energy Conservation Law. The new system are then discretized by the conventional finite difference method and a semi-discretized system is obtained, which can conserve the semi-discretized local Energy Conservation Law. Subsequently, the linearly implicit structure-preserving method is applied for the resulting semi-discrete system to arrive at a fully discretized scheme. We prove that the resulting scheme can exactly preserve the discrete local Energy Conservation Law. Moveover, with the aid of the classical Energy method, an unconditional and optimal error estimate for the scheme is established in discrete $H_h^1$-norm. Finally, various numerical examples are addressed to confirm our theoretical analysis and demonstrate the advantage of the new scheme over some existing local structure-preserving schemes.

Ruili Zhang - One of the best experts on this subject based on the ideXlab platform.

  • local Energy Conservation Law for a spatially discretized hamiltonian vlasov maxwell system
    Physics of Plasmas, 2017
    Co-Authors: Jianyuan Xiao, Hong Qin, Jian Liu, Ruili Zhang
    Abstract:

    Because of the unparalleled long-term conservative property, the structure-preserving geometric algorithm for the Vlasov-Maxwell (VM) equations is currently an active research topic. We show that spatially discretized Hamiltonian systems for the VM equations admit a local Energy Conservation Law in space-time. This is accomplished by proving that a sum-free and only locally non-zero scalar field can always be written as the divergence of a vector field that is only locally non-zero. The result demonstrates that the Hamiltonian discretization of Vlasov-Maxwell system can preserve local Conservation Laws, in addition to the symplectic structure, both of which are the intrinsic physical properties of infinite dimensional Hamiltonian systems in physics.

  • local Energy Conservation Law for spatially discretized hamiltonian vlasov maxwell system
    arXiv: Computational Physics, 2016
    Co-Authors: Jianyuan Xiao, Hong Qin, Jian Liu, Ruili Zhang
    Abstract:

    Structure-preserving geometric algorithm for the Vlasov-Maxwell (VM) equations is currently an active research topic. We show that spatially-discretized Hamiltonian systems for the VM equations admit a local Energy Conservation Law in space-time. This is accomplished by proving that for a general spatially-discretized system, a global Conservation Law always implies a discrete local Conservation Law in space-time when the algorithm is local. This general result demonstrates that Hamiltonian discretizations can preserve local Conservation Laws, in addition to the symplectic structure, both of which are the intrinsic physical properties of infinite dimensional Hamiltonian systems in physics.

Hong Qin - One of the best experts on this subject based on the ideXlab platform.

  • local Energy Conservation Law for a spatially discretized hamiltonian vlasov maxwell system
    Physics of Plasmas, 2017
    Co-Authors: Jianyuan Xiao, Hong Qin, Jian Liu, Ruili Zhang
    Abstract:

    Because of the unparalleled long-term conservative property, the structure-preserving geometric algorithm for the Vlasov-Maxwell (VM) equations is currently an active research topic. We show that spatially discretized Hamiltonian systems for the VM equations admit a local Energy Conservation Law in space-time. This is accomplished by proving that a sum-free and only locally non-zero scalar field can always be written as the divergence of a vector field that is only locally non-zero. The result demonstrates that the Hamiltonian discretization of Vlasov-Maxwell system can preserve local Conservation Laws, in addition to the symplectic structure, both of which are the intrinsic physical properties of infinite dimensional Hamiltonian systems in physics.

  • local Energy Conservation Law for spatially discretized hamiltonian vlasov maxwell system
    arXiv: Computational Physics, 2016
    Co-Authors: Jianyuan Xiao, Hong Qin, Jian Liu, Ruili Zhang
    Abstract:

    Structure-preserving geometric algorithm for the Vlasov-Maxwell (VM) equations is currently an active research topic. We show that spatially-discretized Hamiltonian systems for the VM equations admit a local Energy Conservation Law in space-time. This is accomplished by proving that for a general spatially-discretized system, a global Conservation Law always implies a discrete local Conservation Law in space-time when the algorithm is local. This general result demonstrates that Hamiltonian discretizations can preserve local Conservation Laws, in addition to the symplectic structure, both of which are the intrinsic physical properties of infinite dimensional Hamiltonian systems in physics.

Jianyuan Xiao - One of the best experts on this subject based on the ideXlab platform.

  • local Energy Conservation Law for a spatially discretized hamiltonian vlasov maxwell system
    Physics of Plasmas, 2017
    Co-Authors: Jianyuan Xiao, Hong Qin, Jian Liu, Ruili Zhang
    Abstract:

    Because of the unparalleled long-term conservative property, the structure-preserving geometric algorithm for the Vlasov-Maxwell (VM) equations is currently an active research topic. We show that spatially discretized Hamiltonian systems for the VM equations admit a local Energy Conservation Law in space-time. This is accomplished by proving that a sum-free and only locally non-zero scalar field can always be written as the divergence of a vector field that is only locally non-zero. The result demonstrates that the Hamiltonian discretization of Vlasov-Maxwell system can preserve local Conservation Laws, in addition to the symplectic structure, both of which are the intrinsic physical properties of infinite dimensional Hamiltonian systems in physics.

  • local Energy Conservation Law for spatially discretized hamiltonian vlasov maxwell system
    arXiv: Computational Physics, 2016
    Co-Authors: Jianyuan Xiao, Hong Qin, Jian Liu, Ruili Zhang
    Abstract:

    Structure-preserving geometric algorithm for the Vlasov-Maxwell (VM) equations is currently an active research topic. We show that spatially-discretized Hamiltonian systems for the VM equations admit a local Energy Conservation Law in space-time. This is accomplished by proving that for a general spatially-discretized system, a global Conservation Law always implies a discrete local Conservation Law in space-time when the algorithm is local. This general result demonstrates that Hamiltonian discretizations can preserve local Conservation Laws, in addition to the symplectic structure, both of which are the intrinsic physical properties of infinite dimensional Hamiltonian systems in physics.

Jin Cui - One of the best experts on this subject based on the ideXlab platform.

  • arbitrarily high order structure preserving schemes for the gross pitaevskii equation with angular momentum rotation
    Computer Physics Communications, 2021
    Co-Authors: Chaolong Jiang, Yushun Wang, Jin Cui
    Abstract:

    Abstract In this paper, we design a novel class of arbitrarily high-order structure-preserving numerical schemes for the time-dependent Gross–Pitaevskii equation with angular momentum rotation. Based on the idea of the scalar auxiliary variable approach which is proposed in the recent papers [J. Comput. Phys., 353 (2018) 407–416 and SIAM Rev., 61(2019) 474–506] for developing Energy stable schemes for gradient flow systems, we firstly reformulate the Gross–Pitaevskii equation into an equivalent system with a modified Energy Conservation Law. The reformulated system is then discretized by the Gauss collocation method in time and the standard Fourier pseudo-spectral method in space, respectively. We show that the proposed schemes can preserve the discrete mass and modified Energy exactly. Numerical results are addressed to verify the efficiency and high-order accuracy of the proposed schemes.