This study employs the Method of Fundamental Solutions (MFS) in conjunction with the Particle Swarm Optimization (PSO) algorithm as the primary spatial discretization technique to develop a numerical wave tank for investigating wave propagation characteristics and wave–structure interaction phenomena. The MFS is a boundary-type meshless method that requires only boundary points and source points to solve boundary value problems, offering high accuracy and computational efficiency. To enhance the numerical stability of the MFS, the PSO algorithm is utilized to determine the optimal spatial locations of the source points, thereby ensuring accurate simulation results at each time step. Furthermore, to improve computational efficiency, a domain decomposition method is adopted to reduce the computational cost and accelerate the simulation process. In addition to the spatial discretization scheme, several numerical techniques—including the second-order Runge–Kutta method, sponge layer treatment, and the semi-Lagrangian technique—are integrated to construct a fast and stable numerical wave tank. The proposed meshless numerical wave tank is validated through multiple numerical examples, demonstrating its accuracy, stability, and computational efficiency in simulating wave propagation and wave–structure interaction problems.