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 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.Comment: 14 pages, 3 figures, 2 table

Global path planning and waypoint following for heterogeneous unmanned surface vehicles assisting inland water monitoring

The idea of dispatching multiple unmanned surface vehicles (USVs) to undertake marine missions has ignited a burgeoning enthusiasm on a global scale. Embarking on a quest to facilitate inland water monitoring, this paper presents a systematical approach concerning global path planning and path following for heterogeneous USVs. Specifically, by capturing the heterogeneous nature, an extended multiple travelling salesman problem (EMTSP) model, which seamlessly bridges the gap between various disparate constraints and optimization objectives, is formulated for the first time. Then, a novel Greedy Partheno Genetic Algorithm (GPGA) is devised to consistently address the problem from two aspects: (1) Incorporating the greedy randomized initialization and local exploration strategy, GPGA merits strong global and local searching ability, providing high-quality solutions for EMTSP. (2) A novel mutation strategy which not only inherits all advantages of PGA but also maintains the best individual in the offspring is devised, contributing to the local escaping efficiently. Finally, to track the waypoint permutations generated by GPGA, control input is generated by the nonlinear model predictive controller (NMPC), ensuring the USV corresponds with the reference path and smoothen the motion under constrained dynamics. Simulations and comparisons in various scenarios demonstrated the effectiveness and superiority of the proposed scheme