282ed2c38b
Use center-to-center intervals for forward E derivatives and base-cell widths for backward H derivatives in the Gridlock examples. Document the distinction from meshes defined directly by forward intervals and fix the random fixture's backward averaging direction. Add coordinate-derivative regression coverage for graded periodic and nonperiodic Gridlock meshes using both functional and sparse operators. Validation: 1689 tests passed, 586 skipped; no new Ruff findings in changed Python files.
26 lines
938 B
Markdown
26 lines
938 B
Markdown
# fdmath
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For Gridlock's default E-field Yee shifts, construct solver spacings as
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`dxes = [grid.autoshifted_dxyz(), grid.dxyz]`. The forward E curl needs
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distances between adjacent base-cell centers; the backward H curl needs
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distances between adjacent upper cell edges. Reversing these two width families
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introduces an error on graded grids that uniform grids hide.
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If constructing the mesh directly from **forward derivative intervals** `d`,
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with H samples at their midpoints, the backward intervals instead follow
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`(d + numpy.roll(d, 1)) / 2` for periodic boundaries. These `d` arrays are
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already center-to-center distances, whereas `grid.dxyz` contains base-cell
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volume widths. Applying this averaging rule to `grid.dxyz` does not fix the
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ordering error above.
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::: meanas.fdmath
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## Functional and sparse operators
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::: meanas.fdmath.functional
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::: meanas.fdmath.operators
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::: meanas.fdmath.vectorization
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::: meanas.fdmath.types
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