| Issue |
ESAIM: M2AN
Volume 59, Number 3, May-June 2025
|
|
|---|---|---|
| Page(s) | 1747 - 1761 | |
| DOI | https://doi.org/10.1051/m2an/2025042 | |
| Published online | 26 June 2025 | |
A low-rank algorithm for strongly damped wave equations with visco-elastic damping and mass terms
1
School of Mathematical Sciences, Sichuan Normal University, Chengdu, Sichuan 610066, P.R. China
2
School of Mathematics, Southwestern University of Finance and Economics, Chengdu, Sichuan 611130, P.R. China
* Corresponding author: guxianming@live.cn; guxm@swufe.edu.cn
Received:
14
November
2023
Accepted:
23
May
2025
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.
Mathematics Subject Classification: 65L04 / 65L05 / 65N06
Key words: Semilinear wave equations / strong damping / low-rank splitting / dynamical low-rank approximation
© The authors. Published by EDP Sciences, SMAI 2025
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