Indirect Boundary Element Method For Solving Acoustic Scattering Problems In Solid Media

Boundary element method(BEM)is the most commonly used method to study the propagation of sound waves in media.The equation of sound wave or elastic wave propagation in solid medium is more complicated than that in fluid medium.Based on the advantages of the indirect boundary element method,the boundary value problems of wave propagation equations in solid media are studied in this paper.When the boundary element method is used to solve the boundary value problems of differential equations,singular integral operators are often encountered.It is necessary to deal with its singularity in numerical solution,so it is necessary to study the asymptotic property of the kernel function of integral operator.The content of this paper is arranged as follows:1.The basic solutions of the correlative equations of sound wave or elastic wave are all related to Bessel function,which is a special kind of function and often needs to be expressed in the form of series.In this paper,the asymptotic properties of several Bessel functions are studied according to their series expressions,and the specific asymptotic expressions are given.2.According to the asymptotic expression of the Bessel function,the basic solution acoustic and elastic wave equation is studied and the related expression of asymptotic properties of sound waves in a fluid medium are given by the corresponding fundamental solution equation at the singular point of asymptotic results,and the elastic wave propagation equation in solid medium basic solution of displacement and stress in basic solution asymptotic result of singular points.3.The method of solving the motion equation of sound wave or elastic wave in solid and the indirect boundary element under the displacement boundary condition is given.The scattering solution is represented by the potential constructed by the kernel function of the basic displacement solution and the basic stress solution,and then the boundary integral equation is established according to the potential theory and boundary condition.The N ystr¨om method is used to solve the boundary integral equation respectively.Combined with the asymptotic property of the basic solution studied above,the concrete derivation process of parameterization and discretization of the boundary integral equation is given,and the concrete numerical examples are given.The research work in this paper focuses on the application of the boundary element method to the problems related to acoustic waves or elastic waves.The discussion and theoretical derivation of the asymptotic properties of the fundamental solutions of the equations are of great theoretical significance.In addition,the indirect boundary element method is used to solve the boundary value problem of acoustic wave propagation in solid medium,which has certain application value.