For more information about this meeting, contact Victor Nistor, Robin Enderle, Mark Levi, Jinchao Xu, Ludmil Zikatanov.
| Title: | Numerical Approximation of Asymptotically Disappearing Solutions of Maxwell's Equations |
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| Seminar: | CCMA Luncheon Seminar |
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| Speaker: | James Adler, Tufts University Mathematics |
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| Abstract: |
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| 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 |
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| Date: | 02 / 08 / 2013 |
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| Time: | 12:20pm - 01:30pm |
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