Prof. Ralf Hiptmair
ETH-Zentrum Zurich
Coercive Combined Field Integral Equation for Direct Scattering
Abstract: Many boundary integral equation methods used in the simulation of direct acousting or electromagnetic scattering of a time-harmonic wave at a (sound hard or perfectly conducting) obstacle break down, when applied at frequencies close to a resonant frequency of the obstacle. A remedy is offered by special indirect boundary element methods based on the so-called combined field integral equation (CFIE). However, hitherto no general theoretical results about the convergence of discretized combined field integral equations in three dimensions have been available.I am going to propose new combined field integral equations, convert them into variational form, establish their coercivity in the natural trace spaces, and conclude existence and uniqueness of solutions for any frequency. Moreover, a conforming Galerkin discretization of the variational equations by means of boundary elements can be shown to be asymptotically quasi-optimal. This permits me to derive quantitative convergence rates on sufficiently fine, uniformly shape-regular sequences of surface triangulations.
| Zeit: | Friday, Mai 30, 2003, 16.15 Uhr |
| Ort: | FU Berlin, Arnimallee 2-6, Raum 032 im EG |