ICME Seminar: Chrysoula Tsogka

Chrysoula Tsogka

Department of Mathematics

University of Chicago

The fictitious domain method and applications in wave

propagation problems

This work falls within the more general framework of developing efficient

numerical methods for approximating wave propagation in complex media

such as anisotropic heterogeneous media with cracks or objects of

arbitrary shapes. We consider here the case of the elastic

wave equation with a free surface boundary condition on the crack

(or the object). To solve this problem in an efficient way we propose

to use a fictitious domain approach. This method allows

us to work with uniform meshes independent of the geometry of the

cracks (or the objects), the boundary condition being taken into account

via the introduction of a Lagrange multiplier. The robustness of the

method will be illustrated with several numerical results

concerning applications in non destructive testing and seismicwave

propagation.