Hadamard-Babich ansatz for point-source Maxwell's equations

 Speaker: Jianliang Qian (Michigan State University)

We propose a novel Hadamard-Babich ansatz consisting of an infinite series of dyadic coefficients (three-by-three matrices) and spherical Hankel functions for solving point-source Maxwell's equations in an inhomogeneous medium so as to produce the so-called dyadic Green's function. Using properties of spherical Hankel functions, we derive governing equations for the unknown asymptotics of the ansatz including the travel time function and dyadic coefficients. By proposing matching conditions at the point source, we rigorously derive asymptotic behaviors of these geometrical-optics ingredients near the source so that their initial data at the source point are well-defined. To verify the feasibility of the proposed ansatz, we truncate the ansatz to keep only the first two terms, and we further develop partial-differential-equation based Eulerian approaches to compute the resulting asymptotic solutions. Numerical examples demonstrate that our new ansatz yields a uniform asymptotic solution in the region of space containing a point source but no other caustics. 

Time: October 21, 2022 2:30pm-3:30pm
Location: Virtually via Zoom
Host: Lili Ju