A novel boundary integral formulation for the biharmonic wave scattering problem
Abstract
This paper is concerned with the cavity scattering problem in an infinite thin plate, where the out-of-plane displacement is governed by the two-dimensional biharmonic wave equation. Based on an operator splitting, the scattering problem is recast into a coupled boundary value problem for the Helmholtz and modified Helmholtz equations. A novel boundary integral formulation is proposed for the coupled problem. By introducing an appropriate regularizer, the well-posedness is established for the system of boundary integral equations. Moreover, the convergence analysis is carried out for the semi- and full-discrete schemes of the boundary integral system by using the collocation method. Numerical results show that the proposed method is highly accurate for both smooth and nonsmooth examples.
Cite
@article{arxiv.2301.10142,
title = {A novel boundary integral formulation for the biharmonic wave scattering problem},
author = {Heping Dong and Peijun Li},
journal= {arXiv preprint arXiv:2301.10142},
year = {2023}
}