Abstract
The aim of this paper is to introduce an orignal coupling procedure between surface integral equation formulations and on-surface radiation condition (OSRC) methods for solving two-dimensional scattering problems for non convex structures. The key point is that the use of the OSRC introduces a sparse block in the surface operator representation of the wave field while the integral part leads to an improved accuracy of the OSRC method in the non convex part of the scattering structure. The procedure is given for both the Dirichlet and Neumann scattering problems. Some numerical simulations show the improvement induced by the coupling method.
Highlights
During the last decades, time-harmonic wave propagation has proved to be central in many engineering and technological key developments, based, e.g., on acoustics, electromagnetism or elastic mechanisms
When a discretization technique is applied, as the boundary element method, the corresponding discrete version of the integral equation leads to the numerical solution of a highly indefinite complex-valued dense linear system which is difficult to tackle in the high-frequency regime
Since the on-surface radiation condition (OSRC) solution is locally inaccurate in the non convex part of the domain, we propose to build a solution which is computed first by the OSRC method and improved thanks to the integral equation where the quality of the OSRC approximation deteriorates
Summary
Time-harmonic wave propagation has proved to be central in many engineering and technological key developments, based, e.g., on acoustics, electromagnetism or elastic mechanisms. One well-known possibility is to use an absorbing boundary condition [1,2,3,4,5,6,7] or a Perfectly Matched Layer [8,9,10,11,12,13] to bound the domain and solve the resulting problem by the finite element method [14,15,16] Another widely used alternative is to rewrite equivalently the initial exterior PDE problem as an integral equation over the finite surface Γ of the scatterer Ω− based on the Green’s function [17,18,19,20,21,22,23,24,25,26,27,28].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
