| Speaker: | Francisco-Javier Sayas, Universidad de Zaragoza (Spain) & University of Minnesota |
| Title: | BEM-FEM operators in the resolvent set of the Laplacian and scattering of transient waves |
| Time: | 3:00-4:00 pm |
| Place: | Blocker 628 |
A longer title for this talk gives more information about its contents: Estimates for boundary-field (BEM-FEM) discretizations in the resolvent set of the Laplace operator and applications to the use of convolution quadrature for simulation of the scattering of transient waves by penetrable obstacles. The Convolution Quadrature method, devised by Christian Lubich in the late eighties in a frame of discrete operator calculus, offers interesting chances for the numerical approximation of some complicated time-convolution equations such as those related to retarded potentials. The method combines the use of data in time with the Laplace transform of the operator and has been used in combination with boundary elements for scattering of elastic waves in cases where the fundamental solution in time domain is not known. In the realm of wave propagation, CQ has been almost exclusively used for exterior boundary value problems. In this talk I will address the theoretical difficulties that arise when we try to use this method for scattering problems with penetrable (possibly non-homogeneous) obstacles. I will relate this question to the possibility of showing bounds for the resolvent of some BEM-FEM operators and I will try to illustrate some novel analytical techniques to approach this problem.
Last revised: 04/28/08 By: abnersg@math