Numerical simulation of water wave forces on the the sonic barriers to the numerical solution of the inverse scattering problem and twodimensional large scale cylinder 

Author  ZhangMeiDong 
Tutor  WangLianTang 
School  Northwestern University 
Course  Applied Mathematics 
Keywords  Far field Layer potential theory Tikhonov Regularization method Obstacle inverse scattering Recover Droped corner Wave roll 
CLC  O427.2 
Type  Master's thesis 
Year  2007 
Downloads  94 
Quotes  0 
The inverse problem of "finding the cause or inverse image (input) from known effect or behavior (output)", which named as "the inverse problems of the mathematics and physics" have been proposed in many research fields of science and technology.The inverse acoustic scattering problem is the typical one of those inverse problems,and it has many important uses in all kinds of fields,such as undamaged inspection ,medicine imaging, tracking radar and resources exploration of petroleum,mineral and ocean.Water wave numerical simulation is also a typical mathematics physics inverse problem,and it has important guidance for irrigation works,coast works,ocean and enviroments.Dails are as follows:Firstly,in acoustic direct scattering problems,this article uses layer potential theory for Dirichlet boundary condition, Impedance boundary condition,Neumann boundary condition to translate direct problems into the second Fredholm boundary integral equations;then it uses expectedly Nystrom method,Collocation method,Galerkin method to seek the solutions of those boundary integral equations.As a result,the numerical solutions of the direct scattering problems are obtained.Further,a comparison result is also given by experiment examples.Secondly,in acoustic inverse scattering problems,this article carries through reconstruction for scattering regions with a corner.Since the problem is nonlinear and illposed,then it is turned into a minimizing problem by using the Tikhonov Regularization method;and the quasiNewton method is used to solve the problem and give an approximation to the scattering boundary.So the modification of singleand doublelayer potential is used to approach scattering wave, and a graded mesh integral is use because of the singularity,so error in droped corner minimizes greatly.Then this article proves convergence for this method,Very good result is obtained by examples.Lastly,in water wave numerical simulation,this article prosects numerical simulation for larger scale squat wave billow power.linearity small swing breadth theory is used to translate water wave roll problem into a two dimensional Helmholtz equation, the comparison of numerical solution and parse solution by this method indates good precision.Accurate precision simulation is obained by experiment example.While the construction with no column ,it is difficult to bain parse solution ,this article gives only numerical solution.