A novel boundary integral formulation for the biharmonic wave scattering problem

TL;DR

This paper introduces a new boundary integral formulation for the biharmonic wave scattering problem in thin plates, combining operator splitting and regularization to achieve high accuracy and well-posedness.

Contribution

It presents a novel boundary integral approach for biharmonic wave scattering, with proven well-posedness and convergence analysis, enhancing numerical accuracy for complex geometries.

Findings

High accuracy for smooth and nonsmooth examples

Well-posedness established through regularization

Convergence demonstrated for semi- and full-discrete schemes

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.