A low-rank algorithm for strongly damped wave equations with visco-elastic damping and mass terms

Damped wave equations have been used in many real-world simulations. In this paper, we study a low-rank solution method 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 system of second-order matrix differential equations. Next, we transform it into an equivalent system of first-order matrix differential equations, and split the transformed system into three subproblems. Applying a Strang splitting to such 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 the second-order convergence rate in time.