A Linearly-Implicit Structure-Preserving Exponential Time Differencing Scheme for Hamiltonian PDEs (Journal of Computational Mathematics, 2024)
In the paper, we propose a novel linearly implicit structure-preserving algorithm, whichis derived by combing the invariant energy quadratization approach with the exponentialtime differencing method, to construct efficient and accurate time discretization scheme fora large class of Hamiltonian partial differential equations (PDEs). The proposed schemeis a linear system, and can be solved more efficient than the original energy-preserving exponential integrator scheme which usually needs nonlinear iterations. Various experimentsare performed to verify the conservation, efficiency and good performance at relativelylarge time step in long time computations.
Keywords: Structure-preserving algorithm; Hamiltonian PDE; Energy quadratization method; Exponential time differencing.