'Field' in Bistatic RCS tutorial

Applications
1

Hi Bempp.

Near the end of the Bistatic RCS tutorial there’s a line of code:
exterior_values = -epot0_ext * sol[1] - mpot0_ext * sol[0]
I think exterior_values is an array of electric field (E) values in the host medium (the vacuum in which the two dielectric spheres are placed) due to sphere0. But, even though I’ve tried really hard to work it out, I’m not 100% sure it’s E (rather than H or E+H).

Is it E? What is the analogous expression for the magnetic field H? In fact, what would be really helpful would be to have:
EextFromSphere0=
HextFromSphere0=
EintForSphere0=
HintForSphere0=
Can you please give the missing right-hand-sides for these four lines of code. In your answer, can you please include eps_rv and mu_rv, the relative permittivity and permeability for the vacuum, because then I will be able to figure out how the lines of code will need to be modified if the host medium is something other than the vacuum.

I think once I have these four lines of code I will be ready to start doing some calculations of my own, but, until I have the four lines of code, I fear I’m a bit stuck. So I do hope you can help.

Yours sincerely,

David Wardle.

2

Maybe I’ve seen the light…

Please ignore my request for help while I run some tests to see if my hunch is correct. I’ll then post an update.

3

David,

This line of code implements the Stratton-Chu representation formula for the electric field, in terms of the surface current density.

You can find more information in, e.g., Eq. (23) in Redirecting. Notice that the code examples in that paper are for Bempp v.3 but bempp-cl is very similar.

Best,
Elwin

4

Hi, It seems to me, there is an inaccuracy in the description in Bistatic RCS tutorial: 1) It should be γtHj−=γtHj+ instead of Hj−=Hj+ and 2) It should be Vjinc=Vj+ - Vjs instead of Vjinc=Vj+ + Vjs. If I’m not right please ignore this message.

5

I agree with you, piman (although I’m no Bempp expert).

Also, near the beginning of the tutorial:
‘…the normal trace γtE=E×n and the Neumann trace γN=1/ik γt[∇×E]. The exterior field Es is the sum of the…’ should be (?) ‘…the normal trace γtE=E×n and the Neumann trace γNE=1/ik γt[∇×E]. The exterior field E is the sum of the…’ (one E added after γN and one superscript s removed). I would also question the use of the word ‘normal’ here as this can mean either ‘usual’ or ‘perpendicular’ — it’s not clear to me which is meant.

I hope this is helpful,

David Wardle.

6

Hi, David, I also agree with you. ‘E’ symbol looks lost in the definition of Neumann trace. Exterior field is E+, not Es. And as far as I know, γtE is a tangential trace, not a normal trace. Hope you find this helpful.

Vladimir Pimanov