jan/fdfd_tools
2
2
Fork 1
Code Issues Pull Requests Releases Wiki Activity

grid figure fixup

Browse Source
This commit is contained in:
Jan Petykiewicz 2020-01-04 18:19:04 -08:00
parent e69201ce24
commit a8364a1e32
1 changed files with 85 additions and 73 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

158
meanas/fdmath/__init__.py
View File

@ -387,41 +387,43 @@ to make the illustration simpler; we need at least two cells in the x dimension
demonstrate how nonuniform `dx` affects the various components. demonstrate how nonuniform `dx` affects the various components.
Place the E fore-vectors at integer indices \\( r = (m, n, p) \\) and the H back-vectors Place the E fore-vectors at integer indices \\( r = (m, n, p) \\) and the H back-vectors
at fractional indices \\( r + \\frac{1}{2} = (m + \\frac{1}{2}, n + \\frac{1}{2}, p + \\frac{1}{2}. at fractional indices \\( r + \\frac{1}{2} = (m + \\frac{1}{2}, n + \\frac{1}{2},
Remember that these are indices and not coordinates; they can coorespond to arbitrary p + \\frac{1}{2}) \\). Remember that these are indices and not coordinates; they can
(monotonically increasing) coordinates depending on the cell widths. correspond to arbitrary (monotonically increasing) coordinates depending on the cell widths.
Draw lines to denote the planes on which the H components and back-vectors are defined. Draw lines to denote the planes on which the H components and back-vectors are defined.
For simplicity, don't draw the equivalent planes for the E components and fore-vectors, For simplicity, don't draw the equivalent planes for the E components and fore-vectors,
except as necessary to show their locations -- it's easiest to just connect them to their except as necessary to show their locations -- it's easiest to just connect them to their
associated H-equivalents. The result looks something like this: associated H-equivalents.
The result looks something like this:
[figure: Component centers] [figure: Component centers]
p= p=
[H]__________Hx___________[H]______Hx______[H] __ +1/2 [H]__________Hx___________[H]_____Hx______[H] __ +1/2
z y /: /: /: /: /| | | z y /: /: /: /: /| | |
|/_x / : / : / : / : / | | | |/_x / : / : / : / : / | | |
/ : / : / : / : / | | | / : / : / : / : / | | |
Hy : Ez...........Hy : Ez......Hy | | | Hy : Ez...........Hy : Ez......Hy | | |
/: : : : /: : : : /| | | | /: : : : /: : : : /| | | |
/ : Hz : Ey....../.:..Hz : Ey./.|..Hz __ 0 | dz[0] / : Hz : Ey....../.:..Hz : Ey./.|..Hz __ 0 | dz[0]
/ : /: : / / : /: : / / | /| | | / : /: : / / : /: : / / | /| | |
/_________________________/________________/ | / | | | /_________________________/_______________/ | / | | |
| :/ : :/ | :/ : :/ | |/ | | | | :/ : :/ | :/ : :/ | |/ | | |
| Ex : [E].......|..Ex : [E]..|..Ex | | | | Ex : [E].......|..Ex : [E]..|..Ex | | |
| : | : | | | | | : | : | | | |
| [H]..........Hx....|......[H].....Hx|......[H] __ --------- (m=+1/2, p=-1/2) | [H]..........Hx....|......[H].....H|x.....[H] __ --------- (n=+1/2, p=-1/2)
| / | / | / / / | / | / | / / /
| / | / | / / / Hz / Hz / Hz / / /
Hz / Hz / Hz / / / | / | / | / / /
| Hy | Hy | Hy __ 0 / dy[0] | Hy | Hy | Hy __ 0 / dy[0]
| / | / | / / / | / | / | / / /
| / | / | / / / | / | / | / / /
|/ |/ |/ / / |/ |/ |/ / /
[H]__________Hx___________[H]______Hx______[H] __ -1/2 / [H]__________Hx___________[H]_____Hx______[H] __ -1/2 /
=n =n
|------------|------------|--------|------| |------------|------------|-------|-------|
-1/2 0 +1/2 +1 +3/2 = m -1/2 0 +1/2 +1 +3/2 = m
------------------------- ---------------- ------------------------- ----------------
dx[0] dx[1] dx[0] dx[1]
@ -438,36 +440,40 @@ what volumes those components are responsible for representing. Consider the Ex
two of its nearest neighbors are E fore-vectors, labeled `[E]` in the figure. two of its nearest neighbors are E fore-vectors, labeled `[E]` in the figure.
[figure: Ex volumes] [figure: Ex volumes]
<__________________________________________> p=
z y << /: / /: >> | <_________________________________________> __ +1/2
|/_x < < / : / / : > > | z y << /: / /: >> | |
< < / : / / : > > | |/_x < < / : / / : > > | |
< < / : / / : > > | < < / : / / : > > | |
<: < / : : / : >: > | < < / : / / : > > | |
< : < / : : / : > : > | dz[0] <: < / : : / : >: > | |
< : < / : : / : > : > | < : < / : : / : > : > __ 0 | dz[0]
<____________/_____________________________> : > | < : < / : : / :> : > | |
< : < | : :| : > : > | <____________/____________________/_______> : > | |
< Ex < | : Ex| : > Ex > | < : < | : : | > : > | |
< : < | : :| : > : > | < Ex < | : Ex | > Ex > | |
< : <....|.......:........:|.......:...>...:...> < : < | : : | > : > | |
< : < | / :| / / > : > / < : <....|.......:........:...|.......>...:...> __ --------- (n=+1/2, p=-1/2)
< : < | / :| / / > : > / < : < | / : /| /> : > / /
< :< | / :|/ / > :> / < : < | / : / | / > : > / /
< < | / :| / > > / < :< | / :/ | / > :> / /
< < | / | / > > / dy[0] < < | / : | / > > _ 0 / dy[0]
< < | / | / > > / < < | / | / > > / /
<< |/ |/ >> / < < | / | / > > / /
<____________|_________________|___________> / << |/ |/ >> / /
<____________|____________________|_______> __ -1/2 /
=n
|------------|------------|-------|-------|
-1/2 0 +1/2 +1 +3/2 = m
~------------ ----------------- -----------~ ~------------ -------------------- -------~
dx'[-1] dx'[0] dx'[1] dx'[-1] dx'[0] dx'[1]
The Ex values are positioned on the x-faces of the base The Ex values are positioned on the x-faces of the base
grid. They represent the Ex field in volumes shifted by grid. They represent the Ex field in volumes shifted by
a half-cell in the x-dimension, as shown here. Only the a half-cell in the x-dimension, as shown here. Only the
center cell is fully shown; the other two are truncated center cell (with width dx'[0]) is fully shown; the
(shown using >< markers). other two are truncated (shown using >< markers).
Note that the Ex positions are the in the same positions Note that the Ex positions are the in the same positions
as the previous figure; only the cell boundaries have moved. as the previous figure; only the cell boundaries have moved.
@ -477,28 +483,34 @@ two of its nearest neighbors are E fore-vectors, labeled `[E]` in the figure.
center cell here. center cell here.
[figure: Hy volumes] [figure: Hy volumes]
z y mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm s p=
|/_x << m: m: >> | z y mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm __ +1/2 s
< < m : m : > > | dz'[1] |/_x << m: m: >> | |
Hy............m...........Hy........m......Hy > | < < m : m : > > | | dz'[1]
< < m : m : > > | < < m : m : > > | |
< < m : m : > > | Hy........... m........Hy...........m......Hy > | |
< _______m_____:_______________m_____:_>______ < < m : m : > > | |
mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm > | < ______ m_____:_______________m_____:_>______ __ 0
< < | / : | / :> > | < < m /: m / > > | |
< < | / : | / :> > | dz'[0] mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm > | |
< < | / : | / :> > | < < | / : | / > > | | dz'[0]
< wwwwww|w/wwwwwwwwwwwwwwwwwww|w/wwwww>wwwwwww s < < | / : | / > > | |
< < |/ w |/ w > > / < < | / : | / > > | |
_____________|_____________________|________ > / < wwwww|w/wwwwwwwwwwwwwwwwwww|w/wwwww>wwwwwwww __ s
< Hy........|...w...........Hy....|...w...>..Hy / < < |/ w |/ w> > / /
< < | w | w > > / dy[0] _____________|_____________________|________ > / /
< < | w | w > > / < < | w | w > > / /
<< |w |w >> / < Hy........|...w........Hy.......|...w...>..Hy _ 0 / dy[0]
wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww < < | w | w > > / /
<< | w | w > > / /
< |w |w >> / /
wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww __ -1/2 /
|------------|------------|--------|-------|
-1/2 0 +1/2 +1 +3/2 = m
~------------ --------------------- -------~ ~------------ --------------------- -------~
dx'[-1] dx'[0] dx'[1] dx'[-1] dx'[0] dx'[1]
The Hy values are positioned on the y-edges of the base The Hy values are positioned on the y-edges of the base
grid. Again here, the 'Hy' labels represent the same points grid. Again here, the 'Hy' labels represent the same points