PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Stephanie Zerby, Mark Levi, Jinchao Xu.

Title:Numerical Approximation of Asymptotically Disappearing Solutions of Maxwell's Equations
Seminar:CCMA Luncheon Seminar
Speaker:James Adler, Tufts University Mathematics
This work is on the numerical approximation of incoming solutions to Maxwell's equations, whose energy decays exponentially with time (asymptotically disappearing), meaning that the leading term of the back-scattering matrix becomes negligible. For the exterior of a sphere, such solutions are obtained by Colombini, Petkov and Rauch by specifying a maximal dissipative boundary condition on the sphere and setting appropriate initial conditions. We consider a mixed finite element approximation of Maxwell's equations in the exterior of a polyhedron whose boundary approximates the sphere. We use the standard Nedelec-Raviart-Thomas elements and a Crank-Nicholson scheme to approximate the electric and magnetic fields. We set discrete initial conditions with standard interpolation, modified so that these initial conditions are divergence-free. We prove that with such initial conditions, the fully discrete approximation to the electric field is weakly divergence-free for all time. We show numerically that the finite-element solution approximates well the asymptotically disappearing solutions constructed analytically when the mesh size becomes small.

Room Reservation Information

Room Number:MB114
Date:02 / 08 / 2013
Time:12:20pm - 01:30pm