Acoustic Scattering Study Of The Fredholm Integral Equation

Over the past two decades,for one important branch of the inverse problems,in the field of acoustic scattering Problem,the research of the direct Problem,which has lots of numerical solutions, much maturer than the inverse one.The author mainly study the numerical solutions of the direct problems with the Impedance boundary condition and the Neumann boundary condition.The problem with Impedance boundary condition,which is changed to be the second boundary inte-gral equation arising from the layer potential theory approaching the Helmholtz equa-tion, solved by the method of amount.At the same time, it uses radial function ap-proximation "scattered" waves to seek the solution of the Neumann boundary condi-tion.Finally,some numerical examples are presented to show the performance of methods mentioned above.In addition, based on Tikhonov regularization,a numerical algorithm is proposed of Fredholm integral equation.And numerical experiments explain the effective and stability of the algorithm.