Damped wave equations have been used in many real-world fields. In this paper, we study a low-rank solution of the strongly damped wave equation with the damping term, visco-elastic damping term and mass term. Firstly, a second-order finite difference method is employed for spatial discretization. Then, we receive a second-order matrix differential system. Next, we transform it into an equivalent first-order matrix differential system, and split the transformed system into three subproblems. Applying a Strang splitting to these subproblems and combining a dynamical low-rank approach, we obtain a low-rank algorithm. Numerical experiments are reported to demonstrate that the proposed low-rank algorithm is robust and accurate, and has second-order convergence rate in time.

翻译：阻尼波动方程已广泛应用于多个实际领域。本文研究带有阻尼项、粘弹性阻尼项和质量项的强阻尼波动方程的低秩解法。首先采用二阶有限差分法进行空间离散，得到二阶矩阵微分系统。接着将其转化为等价的一阶矩阵微分系统，并将转化后的系统分裂为三个子问题。通过对这些子问题应用Strang分裂并结合动态低秩方法，我们得到一种低秩算法。数值实验表明，所提出的低秩算法具有鲁棒性和精确性，且时间方向上达到二阶收敛率。