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grid figure fixup

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Jan Petykiewicz 4 years ago
parent e69201ce24
commit a8364a1e32
1 changed files with 85 additions and 73 deletions
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158
meanas/fdmath/__init__.py
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@ -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.
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}.
Remember that these are indices and not coordinates; they can coorespond to arbitrary
(monotonically increasing) coordinates depending on the cell widths.
at fractional indices \\( r + \\frac{1}{2} = (m + \\frac{1}{2}, n + \\frac{1}{2},
p + \\frac{1}{2}) \\). Remember that these are indices and not coordinates; they can
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.
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
associated H-equivalents. The result looks something like this:
associated H-equivalents.
The result looks something like this:
[figure: Component centers]
p=
[H]__________Hx___________[H]______Hx______[H] __ +1/2
z y /: /: /: /: /| | |
|/_x / : / : / : / : / | | |
/ : / : / : / : / | | |
Hy : Ez...........Hy : Ez......Hy | | |
/: : : : /: : : : /| | | |
/ : Hz : Ey....../.:..Hz : Ey./.|..Hz __ 0 | dz[0]
/ : /: : / / : /: : / / | /| | |
/_________________________/________________/ | / | | |
| :/ : :/ | :/ : :/ | |/ | | |
| Ex : [E].......|..Ex : [E]..|..Ex | | |
| : | : | | | |
| [H]..........Hx....|......[H].....Hx|......[H] __ --------- (m=+1/2, p=-1/2)
| / | / | / / /
| / | / | / / /
Hz / Hz / Hz / / /
| Hy | Hy | Hy __ 0 / dy[0]
| / | / | / / /
| / | / | / / /
|/ |/ |/ / /
[H]__________Hx___________[H]______Hx______[H] __ -1/2 /
p=
[H]__________Hx___________[H]_____Hx______[H] __ +1/2
z y /: /: /: /: /| | |
|/_x / : / : / : / : / | | |
/ : / : / : / : / | | |
Hy : Ez...........Hy : Ez......Hy | | |
/: : : : /: : : : /| | | |
/ : Hz : Ey....../.:..Hz : Ey./.|..Hz __ 0 | dz[0]
/ : /: : / / : /: : / / | /| | |
/_________________________/_______________/ | / | | |
| :/ : :/ | :/ : :/ | |/ | | |
| Ex : [E].......|..Ex : [E]..|..Ex | | |
| : | : | | | |
| [H]..........Hx....|......[H].....H|x.....[H] __ --------- (n=+1/2, p=-1/2)
| / | / | / / /
Hz / Hz / Hz / / /
| / | / | / / /
| Hy | Hy | Hy __ 0 / dy[0]
| / | / | / / /
| / | / | / / /
|/ |/ |/ / /
[H]__________Hx___________[H]_____Hx______[H] __ -1/2 /
=n
|------------|------------|--------|------|
-1/2 0 +1/2 +1 +3/2 = m
|------------|------------|-------|-------|
-1/2 0 +1/2 +1 +3/2 = m
------------------------- ----------------
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.
[figure: Ex volumes]
<__________________________________________>
z y << /: / /: >> |
|/_x < < / : / / : > > |
< < / : / / : > > |
< < / : / / : > > |
<: < / : : / : >: > |
< : < / : : / : > : > | dz[0]
< : < / : : / : > : > |
<____________/_____________________________> : > |
< : < | : :| : > : > |
< Ex < | : Ex| : > Ex > |
< : < | : :| : > : > |
< : <....|.......:........:|.......:...>...:...>
< : < | / :| / / > : > /
< : < | / :| / / > : > /
< :< | / :|/ / > :> /
< < | / :| / > > /
< < | / | / > > / dy[0]
< < | / | / > > /
<< |/ |/ >> /
<____________|_________________|___________> /
p=
<_________________________________________> __ +1/2
z y << /: / /: >> | |
|/_x < < / : / / : > > | |
< < / : / / : > > | |
< < / : / / : > > | |
<: < / : : / : >: > | |
< : < / : : / : > : > __ 0 | dz[0]
< : < / : : / :> : > | |
<____________/____________________/_______> : > | |
< : < | : : | > : > | |
< Ex < | : Ex | > Ex > | |
< : < | : : | > : > | |
< : <....|.......:........:...|.......>...:...> __ --------- (n=+1/2, p=-1/2)
< : < | / : /| /> : > / /
< : < | / : / | / > : > / /
< :< | / :/ | / > :> / /
< < | / : | / > > _ 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
grid. They represent the Ex field in volumes shifted by
a half-cell in the x-dimension, as shown here. Only the
center cell is fully shown; the other two are truncated
(shown using >< markers).
center cell (with width dx'[0]) is fully shown; the
other two are truncated (shown using >< markers).
Note that the Ex positions are the in the same positions
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.
[figure: Hy volumes]
z y mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm s
|/_x << m: m: >> |
< < m : m : > > | dz'[1]
Hy............m...........Hy........m......Hy > |
< < m : m : > > |
< < m : m : > > |
< _______m_____:_______________m_____:_>______
mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm > |
< < | / : | / :> > |
< < | / : | / :> > | dz'[0]
< < | / : | / :> > |
< wwwwww|w/wwwwwwwwwwwwwwwwwww|w/wwwww>wwwwwww s
< < |/ w |/ w > > /
_____________|_____________________|________ > /
< Hy........|...w...........Hy....|...w...>..Hy /
< < | w | w > > / dy[0]
< < | w | w > > /
<< |w |w >> /
wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww
p=
z y mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm __ +1/2 s
|/_x << m: m: >> | |
< < m : m : > > | | dz'[1]
< < m : m : > > | |
Hy........... m........Hy...........m......Hy > | |
< < m : m : > > | |
< ______ m_____:_______________m_____:_>______ __ 0
< < m /: m / > > | |
mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm > | |
< < | / : | / > > | | dz'[0]
< < | / : | / > > | |
< < | / : | / > > | |
< wwwww|w/wwwwwwwwwwwwwwwwwww|w/wwwww>wwwwwwww __ s
< < |/ w |/ w> > / /
_____________|_____________________|________ > / /
< < | w | w > > / /
< Hy........|...w........Hy.......|...w...>..Hy _ 0 / dy[0]
< < | 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
grid. Again here, the 'Hy' labels represent the same points

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