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explain dx_lists_t

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Jan Petykiewicz 2020-01-04 18:19:57 -08:00
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meanas/fdmath/__init__.py
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@ -533,9 +533,43 @@ are shifted in two dimensions (x and z) compared to the base grid.
directions).
TODO: explain dxes
Datastructure: dx_lists_t
-------------------
In this documentation, the E fore-vectors are placed on the base grid. An
equivalent formulation could place the H back-vectors on the base grid instead.
However, in the case of a non-uniform grid, the operation to get from the "base"
cell widths to "derived" ones is not its own inverse.
The base grid's cell sizes could be fully described by a list of three 1D arrays,
specifying the cell widths along all three axes:
[dx, dy, dz] = [[dx[0], dx[1], ...], [dy[0], ...], [dz[0], ...]]
Note that this is a list-of-arrays rather than a 2D array, as the simulation domain
may have a different number of cells along each axis.
Knowing the base grid's cell widths and the boundary conditions (periodic unless
otherwise noted) is enough information to calculate the cell widths `dx'`, `dy'`,
and `dz'` for the derived grids.
However, since most operations are trivially generalized to allow either E or H
to be defined on the base grid, they are written to take the a full set of base
and derived cell widths, distinguished by which field they apply to rather than
their "base" or "derived" status. This removes the need for each function to
generate the derived widths, and makes the "base" vs "derived" distinction
unnecessary in the code.
The resulting data structure containing all the cell widths takes the form of a
list-of-lists-of-arrays. The first list-of-arrays provides the cell widths for
the E-field fore-vectors, while the second list-of-arrays does the same for the
H-field back-vectors:
[[[dx_e[0], dx_e[1], ...], [dy_e[0], ...], [dz_e[0], ...]],
[[dx_h[0], dx_h[1], ...], [dy_h[0], ...], [dz_h[0], ...]]]
where `dx_e[0]` is the x-width of the `m=0` cells, as used when calculating dE/dx,
and `dy_h[0]` is the y-width of the `n=0` cells, as used when calculating dH/dy, etc.
"""