An iterative method to solve acoustic scattering problems using a boundary integral equation.

In this work, a simple iterative method to solve the acoustic scattering/radiation problems using the boundary integral equation (BIE) formulation is presented. The operator equation obtained in the BIE formulation is converted into a matrix equation using the well-known method of moments solution procedure. The present method requires much fewer mathematical operations per iteration when compared to other available iterative methods. Further, the present iterative method can easily handle multiple incident fields, a highly desirable feature not available in any other iterative method, much the same way as direct solution techniques. Several numerical examples are presented to illustrate the efficiency and accuracy of the method.

A new method to generate an almost-diagonal matrix in the boundary integral equation formulation.

In this work, a new numerical procedure is developed to generate an almost-diagonal matrix for the solution of boundary integral equation formulation dealing with acoustic scattering problems. The major drawback of the traditional boundary integral equation procedure resulting in a dense system matrix is eliminated in this new procedure by grouping the basis functions into a cluster. The geometry of the structure is modeled by planar triangles and the basis functions are defined on the nodes. By doing so, one can get a benefit of a smaller size matrix to begin with. Furthermore, by grouping these node-based basis functions into a cluster, an almost-diagonal matrix is generated. Thus, the solution procedure developed in this work may be utilized for very large scattering problems since the required computer resources are very low. The solution procedure developed in this work is validated for the scattering cross section of the simple shapes with the closed form solutions wherever available and with the other numerical solution procedures.