Application Of Numerical Methods, And Nystr (?) M Of The Two-dimensional Acoustic Inverse Scattering Problem Method

Inverse problems research originated in the fundamental papers of Tikhonov in the 1960's. Inverse problems have very broad application prospects, widely appear in various fields of the natural sciences and practical engineering and technology, such as sub-surface prospecting, nondestructive material testing, medical CT, seismology, sonar and so on. The inverse acoustic scattering problem is an important branch of the research of the inverse problems. Over the past two decades, from theory to method, the inverse acoustic scattering problem research has been made great progress and a number of effective numerical methods have been proposed. But because of the ill-posedness and complexity of inverse problems, there is still some obstacle between the research and actual applications of the inverse acoustic scattering problems.In this paper, inverse acoustic scattering problems have been studied and some satisfactory conclusions are reached. At the same time, the Nystr(o|¨)m method using to solve the direct scattering problem has been applied to other aspects, practical examples are given. This paper is divided into six parts:The first chapter is introduction, the current status of research in the inverse problems and inverse acoustic scattering problems is reported.The second chapter is The Exterior Problem of Helmholtz Equation, the bases of inverse problem, the direct scattering problem is solved by layer potential theory for Dirichlet boundary, this chapter introduces potential theory and the Nystr(o|¨)m method.The third chapter is A Method of the Inverse Obstacle Scattering Problem, this chapter recover the Dirichlet boundary by Taylor expansion of total field on special boundary.The forth chapter is Acoustic Radiation Problem of 2-D Cavity, it uses single-layer potential to approach to exterior sound pressure, then turns it to the solution to the second kind boundary integral equations by jump relations of the potential theory, and solves it by Nystr(o|¨)m method. Numerical examples illustrate the accuracy of the method.The fifth chapter is An Anisotropic Problem in an Exterior Elliptic Domain, by the coordinate transformation, the potential function and the Nystr(o|¨)m method, the numerical method of this problem is obtain. Some numerical examples are presented to demonstrate the performance of this method.The sixth chapter is Mathematical Model of Wave Force Model for Large Scale Multiple Cylinders, the mathematical model of linear wave diffraction is transformed into a two dimension Helmholtz equation by the airy wave theory. The Nystr(o|¨)m method is used to solve the Helmholtz equation, and the numerical results are reasonable as compared with the analytical solution.