Well-conditioned formulation for open surfaces (Maxwell)

Hi all,

I seek a well-conditioned formulation for electromagnetic scattering on a perfectly conductive screens. In [1] it is proposed several well-conditioned formulations, but as I can see they work only for closed surfaces, and do not work for open surfaces and screens. In [2], it is described, how to adapt Preconditioned EFIE formulation to open surfaces and screens. Preconditioned EFIE is E1 * E2 * x = E1 * b formulation, where E1, E2 are electric field operators. Domain, range and dual to range spaces for (E2, E1) are (RWG, BC), (BC, RWG), (SNC, RBC). For open surfaces, BC functions should incorporate half-barycentric-RWGs associated with the barycentric mesh boundary edges to increase convergence.

Does this or any other methods increasing convergence for open surfaces implemented in bempp-cl or bem++3.3.4?

  1. M.W. Scroggs et al., “Software frameworks for integral equations in electromagnetic scattering based on Calderón identities,” in Computers & Mathematics with Applications, vol. 74, iss. 11, pp. 2897-2914, 2017, https://doi.org/10.1016/j.camwa.2017.07.049.
  2. F. P. Andriulli et al., “A Multiplicative Calderon Preconditioner for the Electric Field Integral Equation,” in IEEE Transactions on Antennas and Propagation, vol. 56, no. 8, pp. 2398-2412, Aug. 2008, https://doi.org/10.1109/TAP.2008.926788.

There’s an open issue to implement the variant of BC spaces for screens/open surfaces (Implement BC spaces on screens · Issue #109 · bempp/bempp-cl · GitHub) that I hope to make some progress on in the next few weeks.

I think these spaces were impelmented in Bempp 3.3.4 so you could run some experiments there in the meantime

I am pleased to see you have prioritized this issue. As I can see, BC space in bem++ 3.3.4 and bempp-cl are similar and does not treat boundaries in desired way.