New Method Enhances Wave Equation Solutions with Moving Boundaries

Researchers Michiel Lassuyt, Emma Vancayseele, Wouter Deleersnyder, David Dudal, Sebbe Stouten, and Koen Van Den Abeele have introduced a new method for solving the one-dimensional wave equation in scenarios where the boundary is moving. Their paper, titled "A Novel Interpolation-Based Method for Solving the One-Dimensional Wave Equation on a Domain with a Moving Boundary," was submitted to arXiv on August 29, 2024, and revised on August 30, 2024.

The study revisits the challenges associated with solving the wave equation, particularly in cases where traditional analytical solutions are not feasible. The authors highlight that while Moore's method, introduced in 1970, provides a framework for such problems, it often requires perturbative expansions that can be limited by the assumption that the boundary position is an analytic function of time. The new approach presented in this paper utilizes interpolation techniques, which are designed to enhance computational efficiency and accuracy, especially when dealing with rapid boundary movements.

The authors propose two variants of their method: one based on a conformal coordinate transformation and another utilizing the method of characteristics. Both variants demonstrate improved performance compared to existing numerical methods, particularly in scenarios requiring evaluations at multiple points in time or space.

This advancement could have significant implications for fields that rely on wave dynamics, such as acoustics, optics, and various engineering applications. The ability to solve the wave equation more efficiently could lead to faster simulations and more accurate models in these areas, potentially benefiting research and practical applications alike.

For further details, the paper can be accessed at arXiv:2408.16483.