Two Kinds Of Method To Reconstruct The Crack Graph

In this paper,we mainly study the acoustic scattering problems, which is com-posed of two cracks,for the sake of simplicity, we consider this problem only in the space of R2.suppose T1,r2are the two cracks(open arc),we investigate the direct and inverse scattering problems of the cracks.Then lead to the following problem:Given f∈H1/2(T1) H1/2(T2),h∈H-1/2(r2), Find a function u∈H1loc(R2\(t)) such that The scattered field U is required to satisfy the Sommerfeld Radiation condition uniformly in x=x/|x|-with r=|x|.For the above problem,we have two research objectives:First,We obtain the existence and uniqueness of the solution of the problem. The uniqueness of the prob-lem is obtained by Rellich lemma. Using the boundary integral equation method, we obtain the existence of solutions for the problem,that is using potential theory,we transformed the problwm into a boundary integral system, then by the Fredholm theory,we obtained the existence and uniqueness of solutions for the boundary inte-gral system,thus obtained the existence of solution for the original problem.Second,we study the problem of the corresponding inverse problem,that is re-construction the two cracks T1and T2by the far field information, due to the com-plexity of the problem, we are given the numerical reconstruction example of a single crack, and the crack is reconstructed and compared by using of the decomposition method and the linear sampling method.