Heat Conduction Equation And Acoustic Scattering, Numerical Calculation,

Popular speaking, the direct problem is a sequence of thinking (for example, we use the reasons of one thing to infer the results), and roughly speaking the so-called inverse problem is the opposite of the direct problem (for example, by the known results, and even some of the findings to determine its model or seek the reason).However, the direct and inverse problem we studied is the relevant problem in the mathematical physics equation. The direct and inverse problem of the acoustic wave scattering and heat conduction equation is the typical problem in the mathematical physics. Therefore, this article is to mainly make numerical calculations for the relevant issues of heat conduction equation and acoustic scattering. The numerical calculations of heat conduction equation Dirichlet problem is carried out through the boundary integral method and the potential theory with the error function; in the section of the acoustic wave scattering Kress transformation, the integral method processing the first class singular kernel and single-layer potential mainly adopted to solve the exterior Dirichlet problem in sharp corner area. In the end, the corresponding numerical examples are listed for the two issues above to prove the feasibility and effectiveness of the method.This article is divided into five parts:The first chapter is introduction, introduction briefly describes the information of the inverse problem and inverse problem of acoustic scattering.The second chapter is the numerical solution of acoustic scattering problem, this chapter describes the prepared knowledge of the acoustic scattering problem, especially describing the numerical methods of the Dirichlet exterior problem:the method of Nystrom.Meanwhile,given the optimization method for the inverse problem of acoustic wave scattering, using it to calculate numerical examples.The third chapter is solving the exterior of Dirichlet problem in Domains With corners with a single-layer potential, we use Kress transformation and processing the first class singular kernal of the integral method, then solving the exterior of Dirichlet problem in domains with corners with a single-layer potential. We can see from the numerical examples this method combined with the use of single-layer and double-layer method is basically the same results. The fourth chapter is heat conduction equation, firstly it introduces the relevant knowledge of the heat conduction equation and the boundary integral method, mainly using the boundary integral method and potential theory for solving the Dirichlet boundary problem and giving the numerical examples.