Acoustic Scattering Problems For The Several Methods And Mathematical Model Of Wave Force Model For Large Scale Cylinder

The field of inverse problem is a relatively new area of Mathematical research, having its origins in the the fundamental papers of Tikhonov in the mid-1960's. In these papers, Tikhonov introduced the regularization methods for linear ill- posed problems. It was realized that inverse problems were ill-posed. The inverse acoustic problem is a typical inverse problem. It has bright future in application on radar and sonar, etc. Before considering it we must have the results of direct problem. The direct problem is, given the incident waves and the scattering boundary, to find the scattered waves and in particular its behavior at large distances, i.e. its far field Pattern .The inverse acoustic problem takes this answer as its starting point and asks what is the incident waves and the scattering boundary, which give rise to such a far field behavior. In this paper, some problems of direct obstacle scattering and inverse scattering problems are investigated, some satisfactory conclusions are reached.Details are as follows:1. Potential theory is used to transfer the exterior boundary value problem into the boundary integral equation of the first kind.A Backus-Gilbert method is presented to solve the time-harmonic acoustic wave scattering problem.Numerical result in two dimension is given.compared with with Nystro m method ,this method has less accuracy ,but compute is more simple.2. The combined Hankel function is used to approach the scattered waves and The inverse time-hormonic acoustic scattering problem is changed into an optimization problem.An approximation method is presented. Numerical examples are given to show that this method is both accurate and simple to use.3.The paper use the date of the far field pattern to determine the shape and impedance coefficient of an obstacle. An approximation method is presented. Numerical examples are given showing that this method is both accurate and simple.4.The paper consideres dirichlet scattering problem of acoustic time-harmonic waves in a inhomogeneous medium.Potential theory is used to transfer the dirichlet scattering problem of acoustic time-harmonic waves in a inhomogeneous medium into Lippmann-Schwinger equation to solve. The paper gets the solution of dirichlet scattering problem of acoustic time-harmonic waves in a inhomogeneous medium by dealing with logarithmic singularity,and numerical example is given.5.Cylinder is one the most common onshore or offshore marine installation. Appropriately calculating the wave loads acting on the Cylinder is important . The paper study calculating of Wave Force for Large Scale Cylinder. Using linear Wave diffraction theory to compute wave force for large scale cylinder , the paper present a method to solve the problem of linear wave diffraction .The mathematical model of linear Wave diffraction is transformed into a two dimension Helmholtz equation by the airy wave theory .The Nystro m method is used to solve the Helmholtz equation .Numerical examples illustrate the accuracy of the method.