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About Conformal (or Contour-Path) FDTD and field nullification on PEC boundaries

peponas

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Consider a rectangular tapered waveguide, reminiscent a horn antenna. Of course, the inclined PEC walls cannot accurately be represented by the Yee grid due to the staircase approximation. Here comes the CFDTD where in the cut-cells, the integral form of Faraday law for H field is applied, instead of the differential one. The nearby electric fields are multiplied by a factor <1, relative to the distance of the PEC wall and the cell coordinates. Electric field inside PEC is set to zero.
That's what I have understood so far.
If I calculate the tangential field exactly on the PEC wall (for example Ey component via interpolation), will it be exactly zero or it will be approximately equal to zero, due to discretization errors?
 

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