Extension of the Debye-Lorenz-Mie Formalism for Electromagnetic Scattering to the Time Domain

Title: Extension of the Debye-Lorenz-Mie Formalism for Electromagnetic Scattering to the Time Domain

 

Speaker: Prof. Shidong JiangNJIT, USA

 

Time: 10:30-11:30am; June 27; 2013

 

Place: Conference Room A404, Department of Mathematical Sciences

 

AbstractThe explicit solution to the scattering problem of time dependent Maxwell equations on a sphere is derived. The derivation of the explicit solution is based on a generalization of Debye potentials for the time harmonic case and reduces the problem to two scalar wave problems - one with the Dirichlet condition and the other with the Robin condition. A high-order and stable numerical scheme is constructed to evaluate the solution at an arbitrary point r outside the unit sphere at any time t > 0, without marching in the whole space-time domain. Several numerical examples are presented to illustrate

the performance of the algorithm. The solution can be served as a reference for checking the accuracy of other numerical methods. More importantly, it will provide some insight towards better integral equation formulations for the wave equation and time-dependent Maxwell equations in a general domain.This is joint work with Leslie Greengard at Courant Institute of New York University and Thomas Hagstrom at Southern Methodist University.

 

ContactZhongyi Huang