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

TL;DR

This paper develops a low-rank numerical algorithm for strongly damped wave equations with visco-elastic damping and mass terms, demonstrating robustness, accuracy, and second-order convergence through numerical experiments.

Contribution

It introduces a novel low-rank algorithm combining Strang splitting and dynamical low-rank approach for complex damped wave equations.

Findings

The algorithm is robust and accurate.

It achieves second-order convergence in time.

Numerical experiments confirm effectiveness.

Abstract

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.