meanas/docs/api/fdmath.md

# fdmath

For Gridlock's default E-field Yee shifts, construct solver spacings as
`dxes = [grid.autoshifted_dxyz(), grid.dxyz]`. The forward E curl needs
distances between adjacent base-cell centers; the backward H curl needs
distances between adjacent upper cell edges. Reversing these two width families
introduces an error on graded grids that uniform grids hide.

If constructing the mesh directly from **forward derivative intervals** `d`,
with H samples at their midpoints, the backward intervals instead follow
`(d + numpy.roll(d, 1)) / 2` for periodic boundaries. These `d` arrays are
already center-to-center distances, whereas `grid.dxyz` contains base-cell
volume widths. Applying this averaging rule to `grid.dxyz` does not fix the
ordering error above.

::: meanas.fdmath

## Functional and sparse operators

::: meanas.fdmath.functional

::: meanas.fdmath.operators

::: meanas.fdmath.vectorization

::: meanas.fdmath.types
[docs] switch generated docs to MkDocs 2026-04-18 15:05:35 -07:00			`# fdmath`

[fdmath] correct Gridlock Yee spacing order 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. 2026-10-28 17:32:21 -07:00			`For Gridlock's default E-field Yee shifts, construct solver spacings as`
			`dxes = [grid.autoshifted_dxyz(), grid.dxyz]`. The forward E curl needs
			`distances between adjacent base-cell centers; the backward H curl needs`
			`distances between adjacent upper cell edges. Reversing these two width families`
			`introduces an error on graded grids that uniform grids hide.`

			If constructing the mesh directly from forward derivative intervals `d`,
			`with H samples at their midpoints, the backward intervals instead follow`
			`(d + numpy.roll(d, 1)) / 2` for periodic boundaries. These `d` arrays are
			already center-to-center distances, whereas `grid.dxyz` contains base-cell
			volume widths. Applying this averaging rule to `grid.dxyz` does not fix the
			`ordering error above.`

[docs] switch generated docs to MkDocs 2026-04-18 15:05:35 -07:00			`::: meanas.fdmath`

			`## Functional and sparse operators`

			`::: meanas.fdmath.functional`

			`::: meanas.fdmath.operators`

			`::: meanas.fdmath.vectorization`

			`::: meanas.fdmath.types`