Structure-preserving linearly implicit exponential integrators are constructed for Hamiltonian partial differential equations with linear constant damping. Linearly implicit integrators are derived by polarizing the polynomial terms of the Hamiltonian function and portioning out the nonlinearly of consecutive time steps. They require only a solution of one linear system at each time step. Therefore they are computationally more advantageous than implicit integrators. We also construct an exponential version of the well-known one-step Kahan's method by polarizing the quadratic vector field. These integrators are applied to one-dimensional damped Burger's, Korteweg-de-Vries, and nonlinear Schr\"odinger equations. Preservation of the dissipation rate of linear and quadratic conformal invariants and the Hamiltonian is illustrated by numerical experiments.

翻译：本文针对具有线性常数阻尼的哈密顿偏微分方程，构造了保持结构的线性隐式指数积分器。通过将哈密顿函数中的多项式项极化，并分配连续时间步中的非线性部分，推导出线性隐式积分器。这类方法每步仅需求解一个线性系统，因此在计算效率上优于隐式积分器。我们还通过极化二次向量场，构造了著名的一步Kahan方法的指数形式。这些积分器被应用于一维阻尼Burgers方程、Korteweg-de-Vries方程和非线性Schrödinger方程。数值实验展示了其对线性与二次共形不变量耗散率以及哈密顿量的保持效果。