Sound Wave Transmission Problems In Multilayered Medium

Acoustic scattering problem is an important branch within the field of the mathematical physics problems. During the decades after the rise of this disci-pline, various kinds of problems of acoustic scattering in a homogeneous dielec-tric have been resolved very well. While the researches of the acoustic scattering problem in the inhomogeneous dielectrics are relatively few. This kind of ques-tions are more complex and more difficult to treat. The purpose of this article is to study the acoustic transmission problem for a cylinder buried in multilayered dielectrics.We are committed to transform the acoustic waves problem into a boundary integral equations. To this end, we redefine the corresponding boundary integral operators as well as the single-and double-layer potentials within multilayercd dielectrics. They are still in line with the basic jump relations and regularity properties of acoustic single-and double-layer potentials. Due to the high com-plexity and difficulty in solving the multilayered transmission problem, we begin the study from the circumstance in two different dielectrics. Applying the method of boundary integral equations and the potentials theory, we prove the posedness of the direct transmission problem, and have been transformed it into a bound-ary integral equations. The integral kernels can be divided into two types. One of them is singular, so we use Nystrom method to deal, and the other does not possess the singularity.In the last part of chapter three, we verify the effectiveness and feasibility of our method via several convincing numerical examples. Based on the result of the problem in two layer dielectrics, it’s easier to extend the conclusion to the multilayered dielectrics problem. In chapter four, we get the conclusion of the multilayered transmission problem, and use the representative numerical examples to confirm it.