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{\"o}dinger equations. Preservation of the dissipation rate of linear and quadratic conformal invariants and the Hamiltonian is illustrated by numerical experiments.

翻译：针对具有线性常数阻尼的哈密顿偏微分方程，本文构造了保结构线性隐式指数型积分器。通过将哈密顿函数的多项式项极化处理，并对相邻时间步的非线性项进行分配，导出了线性隐式积分器。该类方法每时间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。我们还通过对二次向量场极化处理，构造了著名的单步Kahan方法的指数型版本。将这些积分器应用于一维阻尼Burgers方程、Korteweg-de-Vries方程和非线性薛定谔方程。数值实验验证了线性与二次共形不变量耗散率及哈密顿量的守恒性质。