For more information about this meeting, contact Victor Nistor, Mark Levi, Jinchao Xu, Ludmil Zikatanov.
|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
|Date:||02 / 08 / 2013|
|Time:||12:20pm - 01:30pm|