Fix bug in interpolation of epsilon grid from Meep to MPB

[oskooi]

Fixes #1237.

Bug Analysis

The error "invalid dielectric function for MPB" is triggered by MPB's check_maxwell_dielectric() (in maxwell_eps.c:266), which validates that every grid point's inverse-epsilon tensor (eps_inv) is positive-definite.

Root cause (in mpb.cpp, the primary fix)

The meep_mpb_eps callback assembles a 3×3 eps_inv tensor at each MPB grid point by querying Meep's get_chi1inv for 6 independent components. The diagonal components each come from their natural Yee grid positions (Ex grid for chi1inv_xx, Ey grid for chi1inv_yy, Ez grid for chi1inv_zz), which are spatially offset by half a pixel from each other. The off-diagonal components were queried from only one grid — e.g., m01 = chi1inv(Ex, Y, p) used only the Ex grid.

Near a curved material boundary (like a Cylinder), the Ex grid point may sit right at the interface where subpixel averaging produces a large off-diagonal chi1inv_xy, while the Ey grid point (half a pixel away) is inside the high-epsilon material with a small chi1inv_yy. The assembled tensor then has m01² > m00 * m11, failing positive-definiteness.

Fix: Average each off-diagonal component from both relevant Yee grids:

• m01 = 0.5 * (chi1inv(Ex,Y,p) + chi1inv(Ey,X,p))
• m02 = 0.5 * (chi1inv(Ex,Z,p) + chi1inv(Ez,X,p))
• m12 = 0.5 * (chi1inv(Ey,Z,p) + chi1inv(Ez,Y,p))

This produces off-diagonal values consistent with both corresponding diagonal values.

Secondary bug (in monitor.cpp, defensive six)

structure_chunk::get_chi1inv_at_pt has a frequency-dependent code path (entered whenever frequency != 0) that builds a full 3×3 chi1inv tensor using chi1inv[comp_list[com_it]][dir_int][idx] for all three components — but idx was computed via gv.index(c, iloc) for a single component c. On the Yee grid, the same flat index refers to a different spatial location for each component, so this reads wrong data. For non-dispersive materials (no susceptibilities or conductivity), this tensor path is a no-op that only introduces errors.

Fix: Skip the tensor assembly path when no frequency-dependent material properties exist, returning the direct chi1inv[c][d][idx] value instead.

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Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 73.90%. Comparing base (f29a8c7) to head (371d22e).
⚠️ Report is 111 commits behind head on master.
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Additional details and impacted files

@@            Coverage Diff             @@
##           master    #3163      +/-   ##
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+ Coverage   73.81%   73.90%   +0.09%     
==========================================
  Files          18       18              
  Lines        5423     5454      +31     
==========================================
+ Hits         4003     4031      +28     
- Misses       1420     1423       +3     

see 2 files with indirect coverage changes

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