NUMERICAL-ANALYSIS OF RESONANCE POLES ASS OCIATED WITH ACOUSTIC AND ELASTIC-WAVE DIFFRACTION BY A 2-DIMENSIONAL OBSTACLE

This article presents a new approach regarding the resonance poles in the theory of Lax and Phillips, who studied the scattering matrix asso ciated with the wave propagation in an acoustical and unbounded domain Omega, in 2D or 3D. Our approach is based on integral equations, deve loped from rile stationary equations of diffraction : we characterize the resonances as poles in C of a family S of operators. The family T of inverses is explicitly determined, and is analytic. Adapting the fi nite element method to the bounded boundary Gamma of Omega, we develop a way of computing resonances. We also show the numerical convergence , justifying the interest of our approach. From these numerical result s, we propose additional theorems on resonancy repartition in C. Final ly the case of elastic waves is discussed briefly We observe fundament al changes for the disk reflexion, compared to the previous situation. In this setting, we give same numerical results for the rectilinear s lit.