Define the source point in the electromagnetic

Greetings everyone,
I am studying the electromagnetic scattering problem by BEMPP and have seen the example ‘‘Bistatic RSC generated by dielectric spheres’’. Notice that the incident field is given in the form of the plane wave, which is relative simpler compared with the case where the incident field is due to the source point located at some position, say z\in\mathbb{R}^3, In my problem, the incident field is given by the following picture, where Phi is the fundamental solution to the Helmholtz given by 1/(4pi)\frac{e^{ik|x-z|}}{|x-z|}, with k the wavenumber.

I do not know how to define such a incident field. More confused, I do not know how to define the corresponding tangential_trace and the trace_fun, which is of importance for this problem setup.

Thank you so much and look forward to your reply.


this is a classic Hertz dipole. You need to work out the derivatives explicitly and then form the tangential trace. You can find a formula for the electric field with all derivatives worked out for example on page 15 of the book “The Mathematical Theory of Time-Harmonic Maxwell’s Equations : Expansion-, Integral-, and Variational Methods,” by Andreas Kirsch and Frank Hettlich (The Mathematical Theory of Time-Harmonic Maxwell's Equations | SpringerLink).

Best wishes, Tilo Arens

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