PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Jinchao Xu.

Title:Multi-scale approach to evolution equations with applications
Seminar:Computational and Applied Mathematics Colloquium
Speaker:Maarten de Hoop (Purdue)
Abstract:
Wave-equation imaging and wave-equation (reflection) tomography can essentially be expressed in terms of solving particular evolution equations. The underlying model describes the single scattering of waves off discontinuities in a background medium. Here, we are concerned with developing a method that admits background media of limited smoothness, which leads to evolution equations generated by certain pseudodifferential operators. We develop a multi-scale approach to solving such evolution equations, while making use of solution representations based on curvelets. We discuss results concerning the `concentration' of curvelets. We then discuss an approximation of functions following the dyadic parabolic decomposition that leads to sparse representations of initial data, image, and solutions irrespective of scale. Finally, we mention the existence and construction of Fr\'{e}chet derivatives, with respect to the background medium, of the solution operators associated with the evolution equations. Joint research with F. Andersson, M. Carlsson, H. Smith and G. Uhlmann.

Room Reservation Information

Room Number:MB106
Date:11 / 09 / 2007
Time:03:35pm - 04:25pm