Two-dimensional Wave Scattering Problem Of Numerical Solution And Applications

As is a comprehensive research area, the mathematical physics inverse prob-lem has very broad application prospects in such fields as geological explo-ration, remote sensing technology, atmosphere sciences,etc. The acoustic scat-tering problem, an important branch of the inverse problems, has been made great progress over the past two decades, and some satisfactory conclusions are reached.In this paper, the numerical solution for the direct acoustic scattering prob-lem with Impedance and Dirichlet boundary condition is studied. By applying potential theory, the direct acoustic scattering problem is finally transformed into solving the second integral equation. Subsequently, a new method is used to split off the logarithmic kernal and then excellent numerical results are ob-tained by using Nystrom method.At the same time, the solution mentioned above is applied to solve the nu-merical simulation of seismic wave. The seismic wave equation problem in fre-quency domain is transformed into the boundary problems of Helmholtz equation by the Fourier transformation, and is solved more efficiently by using nystrom method.