Replacement of electrodes by sheets of charge
The electrodes will be treated by the program as the sites of infinitesimally thin sheets of charge (see information on the Boundary Element Method.) The electrodes themselves therefore cease to exist, as far as the program is concerned.
The charges are those that would exist on the surfaces of the electrodes.
For an actual thin metal electrode, the charges reside on both sides of the electrode, but these charges can be added together and treated as a single sheet of charge, as far as the calculation of potentials is concerned (if the electrode is thin enough).
A thick electrode must be represented by the set of surfaces that enclose it. The calculated charges then reside on the outer sides of the surfaces. The calculated potential inside a thick electrode will be uniform (within the accuracy of the calculation), as expected for a conductor.
Because the electrodes effectively become sheets of charge, rays can pass through them.