setup.grid.1D: Creates a One-Dimensional Finite Difference Grid
In ReacTran: Reactive Transport Modelling in 1d, 2d and 3d
Description
Usage
Arguments
Value
Author(s)
See Also
Examples
View source: R/setup.grid.1D.R
Description
Subdivides the one-dimensional model domain into one or more zones that
are each sub-divided into grid cells. The resulting grid structure can be
used in the other ReacTran functions.
The grid structure is characterized by the position of the middle of
the grid cells (x.mid) and the position of the interfaces between
grid cells (x.int).
Distances are calculated between the interfaces (dx), i.e. the
thickness of the grid cells. An auxiliary set of distances (dx.aux)
is calculated between the points where the concentrations are specified
(at the center of each grid cell and the two external interfaces).
A more complex grid consisting of multiple zones can be constructed when
specifying the endpoints of ech zone (x.down), the interval length
(L), and the number of layers in each zone (N) as vectors.
In each zone, one can control the grid resolution near the upstream and
downstream boundary.
The grid resolution at the upstream interface changes according to the
power law relation dx[i+1] = min(max.dx.1,p.dx.1*dx[i]),
where p.dx.1 determines the rate of increase and max.dx.1
puts an upper limit on the grid cell size.
A similar formula controls the resolution at the downstream interface.
This allows refinement of the grid near the interfaces.
If only x.up, N and dx.1 are specified, then the grid size
is taken constant = dx.1 (and L=N*dx.1)
Usage
1
2
3
4
5
6
Arguments
x.up
position of the upstream interface; one value [L]
x.down
position of the endpoint of each zone; one value when the
model domain covers only one zone (x.down = position of downstream
interface), or a vector of length M when the model domain is divided into
M zones (x.down[M] = position of downstream interface) [L]
L
thickness of zones; one value (model domain = one zone) or a
vector of length M (model domain = M zones) [L]
N
number of grid cells within a zone; one value or a vector of
length M [-]
dx.1
size of the first grid cell in a zone; one value or a vector
of length M [L]
p.dx.1
power factor controlling the increase in grid cell size near
the upstream boundary; one value or a vector of length M. The default
value is 1 (constant grid cell size) [-]
max.dx.1
maximum grid cell size in the upstream half of the zone;
one value or a vector of length M [L]
dx.N
size of the last grid cell in a zone; one value or a vector
of length M [L]
p.dx.N
power factor controlling the increase in grid cell size near the
downstream boundary; one value or a vector of length M. The default value
is 1 (constant grid cell size) [-]
max.dx.N
maximum grid cell size in the downstream half of the zone;
one value or a vector of length M [L]
x
the object of class grid.1D that needs plotting
...
additional arguments passed to the function plot
Value
a list of type grid.1D containing:
N
the total number of grid cells [-]
x.up
position of the upstream interface; one value [L]
x.down
position of the downstream interface; one value [L]
x.mid
position of the middle of the grid cells;
vector of length N [L]
x.int
position of the interfaces of the grid cells;
vector of length N+1 [L]
dx
distance between adjacent cell interfaces (thickness of grid
cells); vector of length N [L]
dx.aux
auxiliary vector containing the distance between adjacent
cell centers; at the upper and lower boundary calculated as
(x[1]-x.up) and (x.down-x[N]) respectively; vector of
length N+1 [L]
Author(s)
Filip Meysman <filip.meysman@nioz.nl>,
Karline Soetaert <karline.soetaert@nioz.nl>
See Also
tran.1D, for a discretisation of the general transport equation in 1-D
setup.grid.2D for the creation of grids in 2-D
setup.prop.1D, for defining properties on the 1-D grid.
Examples
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
# one zone, constant resolution
(GR <- setup.grid.1D(x.up = 0, L = 10, N = 10))
(GR <- setup.grid.1D(x.up = 0, L = 10, dx.1 = 1))
(GR <- setup.grid.1D(x.up = 0, L = 10, dx.N = 1))
plot(GR)
# one zone, constant resolution, origin not zero
(GR <- setup.grid.1D(x.up = 5, x.down = 10, N = 10))
plot(GR)
# one zone, variable resolution
(GR <- setup.grid.1D(x.up = 0, L = 10, dx.1 = 1, p.dx.1 = 1.2))
(GR <- setup.grid.1D(x.up = 0, L = 10, dx.N = 1, p.dx.N = 1.2))
plot(GR)
# one zone, variable resolution, imposed number of layers
(GR <- setup.grid.1D(x.up = 0, L = 10, N = 6, dx.1 = 1, p.dx.1 = 1.2))
(GR <- setup.grid.1D(x.up = 0, L = 10, N = 6, dx.N = 1, p.dx.N = 1.2))
plot(GR)
# one zone, higher resolution near upstream and downstream interfaces
(GR <- setup.grid.1D(x.up = 0, x.down = 10, dx.1 = 0.1,
p.dx.1 = 1.2, dx.N = 0.1, p.dx.N = 1.2))
plot(GR)
# one zone, higher resolution near upstream and downstream interfaces
# imposed number of layers
(GR <- setup.grid.1D(x.up = 0, x.down = 10, N = 20,
dx.1 = 0.1, p.dx.1 = 1.2,
dx.N = 0.1, p.dx.N = 1.2))
plot(GR)
# two zones, higher resolution near the upstream
# and downstream interface
(GR<-setup.grid.1D(x.up = 0, L = c(5, 5),
dx.1 = c(0.2, 0.2), p.dx.1 = c(1.1, 1.1),
dx.N = c(0.2, 0.2), p.dx.N = c(1.1, 1.1)))
plot(GR)
# two zones, higher resolution near the upstream
# and downstream interface
# the number of grid cells in each zone is imposed via N
(GR <- setup.grid.1D(x.up = 0, L = c(5, 5), N = c(20, 10),
dx.1 = c(0.2, 0.2), p.dx.1 = c(1.1, 1.1),
dx.N = c(0.2, 0.2), p.dx.N = c(1.1, 1.1)))
plot(GR)
Example output
Loading required package: rootSolve
Loading required package: deSolve
Loading required package: shape
$x.up
[1] 0
$x.down
[1] 10
$x.mid
[1] 0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5
$x.int
[1] 0 1 2 3 4 5 6 7 8 9 10
$dx
[1] 1 1 1 1 1 1 1 1 1 1
$dx.aux
[1] 0.5 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.5
$N
[1] 10
attr(,"class")
[1] "grid.1D"
$x.up
[1] 0
$x.down
[1] 10
$x.mid
[1] 0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5
$x.int
[1] 0 1 2 3 4 5 6 7 8 9 10
$dx
[1] 1 1 1 1 1 1 1 1 1 1
$dx.aux
[1] 0.5 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.5
$N
[1] 10
attr(,"class")
[1] "grid.1D"
$x.up
[1] 0
$x.down
[1] 10
$x.mid
[1] 0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5
$x.int
[1] 0 1 2 3 4 5 6 7 8 9 10
$dx
[1] 1 1 1 1 1 1 1 1 1 1
$dx.aux
[1] 0.5 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.5
$N
[1] 10
attr(,"class")
[1] "grid.1D"
$x.up
[1] 5
$x.down
[1] 10
$x.mid
[1] 5.25 5.75 6.25 6.75 7.25 7.75 8.25 8.75 9.25 9.75
$x.int
[1] 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0
$dx
[1] 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
$dx.aux
[1] 0.25 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.25
$N
[1] 10
attr(,"class")
[1] "grid.1D"
$x.up
[1] 0
$x.down
[1] 10
$x.mid
[1] 0.3871196 1.2387828 2.2607786 3.4871736 4.9588476 6.7248564 8.8440670
$x.int
[1] 0.0000000 0.7742393 1.7033264 2.8182309 4.1561164 5.7615789 7.6881339
[8] 10.0000000
$dx
[1] 0.7742393 0.9290871 1.1149045 1.3378854 1.6054625 1.9265550 2.3118661
$dx.aux
[1] 0.3871196 0.8516632 1.0219958 1.2263950 1.4716740 1.7660088 2.1192105
[8] 1.1559330
$N
[1] 7
attr(,"class")
[1] "grid.1D"
$x.up
[1] 0
$x.down
[1] 10
$x.mid
[1] 1.155933 3.275144 5.041152 6.512826 7.739221 8.761217 9.612880
$x.int
[1] 0.000000 2.311866 4.238421 5.843884 7.181769 8.296674 9.225761
[8] 10.000000
$dx
[1] 2.3118661 1.9265550 1.6054625 1.3378854 1.1149045 0.9290871 0.7742393
$dx.aux
[1] 1.1559330 2.1192105 1.7660088 1.4716740 1.2263950 1.0219958 0.8516632
[8] 0.3871196
$N
[1] 7
attr(,"class")
[1] "grid.1D"
$x.up
[1] 0
$x.down
[1] 10
$x.mid
[1] 0.5000011 1.6013999 2.9261544 4.5195596 6.4360959 8.7412919
$x.int
[1] 0.000000 1.000002 2.202798 3.649511 5.389608 7.482584 10.000000
$dx
[1] 1.000002 1.202795 1.446714 1.740097 2.092976 2.517416
$dx.aux
[1] 0.5000011 1.1013988 1.3247545 1.5934052 1.9165363 2.3051960 1.2587081
$N
[1] 6
attr(,"class")
[1] "grid.1D"
$x.up
[1] 0
$x.down
[1] 10
$x.mid
[1] 1.258708 3.563904 5.480440 7.073846 8.398600 9.499999
$x.int
[1] 0.000000 2.517416 4.610392 6.350489 7.797202 8.999998 10.000000
$dx
[1] 2.517416 2.092976 1.740097 1.446714 1.202795 1.000002
$dx.aux
[1] 1.2587081 2.3051960 1.9165363 1.5934052 1.3247545 1.1013988 0.5000011
$N
[1] 6
attr(,"class")
[1] "grid.1D"
$x.up
[1] 0
$x.down
[1] 10
$x.mid
[1] 0.04223264 0.13514444 0.24663861 0.38043160 0.54098320 0.73364512
[7] 0.96483942 1.24227258 1.57519237 1.97469612 2.45410062 3.02938601
[13] 3.71972849 4.54813947 5.45186053 6.28027151 6.97061399 7.54589938
[19] 8.02530388 8.42480763 8.75772742 9.03516058 9.26635488 9.45901680
[25] 9.61956840 9.75336139 9.86485556 9.95776736
$x.int
[1] 0.00000000 0.08446528 0.18582361 0.30745361 0.45340960 0.62855680
[7] 0.83873343 1.09094540 1.39359975 1.75678498 2.19260725 2.71559398
[13] 3.34317805 4.09627894 5.00000000 5.90372106 6.65682195 7.28440602
[19] 7.80739275 8.24321502 8.60640025 8.90905460 9.16126657 9.37144320
[25] 9.54659040 9.69254639 9.81417639 9.91553472 10.00000000
$dx
[1] 0.08446528 0.10135833 0.12163000 0.14595600 0.17514720 0.21017664
[7] 0.25221196 0.30265436 0.36318523 0.43582227 0.52298673 0.62758407
[13] 0.75310089 0.90372106 0.90372106 0.75310089 0.62758407 0.52298673
[19] 0.43582227 0.36318523 0.30265436 0.25221196 0.21017664 0.17514720
[25] 0.14595600 0.12163000 0.10135833 0.08446528
$dx.aux
[1] 0.04223264 0.09291180 0.11149416 0.13379300 0.16055160 0.19266192
[7] 0.23119430 0.27743316 0.33291979 0.39950375 0.47940450 0.57528540
[13] 0.69034248 0.82841097 0.90372106 0.82841097 0.69034248 0.57528540
[19] 0.47940450 0.39950375 0.33291979 0.27743316 0.23119430 0.19266192
[25] 0.16055160 0.13379300 0.11149416 0.09291180 0.04223264
$N
[1] 28
attr(,"class")
[1] "grid.1D"
$x.up
[1] 0
$x.down
[1] 10
$x.mid
[1] 0.04999958 0.16661030 0.32196303 0.52892919 0.80465650 1.17198974
[7] 1.66136350 2.31332376 3.18188725 4.33901687 5.66098313 6.81811275
[13] 7.68667624 8.33863650 8.82801026 9.19534350 9.47107081 9.67803697
[19] 9.83338970 9.95000042
$x.int
[1] 0.00000000 0.09999916 0.23322143 0.41070463 0.64715375 0.96215925
[7] 1.38182023 1.94090677 2.68574075 3.67803374 5.00000000 6.32196626
[13] 7.31425925 8.05909323 8.61817977 9.03784075 9.35284625 9.58929537
[19] 9.76677857 9.90000084 10.00000000
$dx
[1] 0.09999916 0.13322226 0.17748320 0.23644912 0.31500551 0.41966098
[7] 0.55908654 0.74483398 0.99229299 1.32196626 1.32196626 0.99229299
[13] 0.74483398 0.55908654 0.41966098 0.31500551 0.23644912 0.17748320
[19] 0.13322226 0.09999916
$dx.aux
[1] 0.04999958 0.11661071 0.15535273 0.20696616 0.27572731 0.36733324
[7] 0.48937376 0.65196026 0.86856349 1.15712963 1.32196626 1.15712963
[13] 0.86856349 0.65196026 0.48937376 0.36733324 0.27572731 0.20696616
[19] 0.15535273 0.11661071 0.04999958
$N
[1] 20
attr(,"class")
[1] "grid.1D"
$x.up
[1] 0
$x.down
[1] 10
$x.mid
[1] 0.09205067 0.28535709 0.49799415 0.73189491 0.98918575 1.27220567
[7] 1.58352758 1.92598169 2.30268121 2.69731879 3.07401831 3.41647242
[13] 3.72779433 4.01081425 4.26810509 4.50200585 4.71464291 4.90794933
[19] 5.09205067 5.28535709 5.49799415 5.73189491 5.98918575 6.27220567
[25] 6.58352758 6.92598169 7.30268121 7.69731879 8.07401831 8.41647242
[31] 8.72779433 9.01081425 9.26810509 9.50200585 9.71464291 9.90794933
$x.int
[1] 0.0000000 0.1841013 0.3866128 0.6093755 0.8544144 1.1239571
[7] 1.4204542 1.7466010 2.1053624 2.5000000 2.8946376 3.2533990
[13] 3.5795458 3.8760429 4.1455856 4.3906245 4.6133872 4.8158987
[19] 5.0000000 5.1841013 5.3866128 5.6093755 5.8544144 6.1239571
[25] 6.4204542 6.7466010 7.1053624 7.5000000 7.8946376 8.2533990
[31] 8.5795458 8.8760429 9.1455856 9.3906245 9.6133872 9.8158987
[37] 10.0000000
$dx
[1] 0.1841013 0.2025115 0.2227626 0.2450389 0.2695428 0.2964971 0.3261468
[8] 0.3587614 0.3946376 0.3946376 0.3587614 0.3261468 0.2964971 0.2695428
[15] 0.2450389 0.2227626 0.2025115 0.1841013 0.1841013 0.2025115 0.2227626
[22] 0.2450389 0.2695428 0.2964971 0.3261468 0.3587614 0.3946376 0.3946376
[29] 0.3587614 0.3261468 0.2964971 0.2695428 0.2450389 0.2227626 0.2025115
[36] 0.1841013
$dx.aux
[1] 0.09205067 0.19330642 0.21263706 0.23390076 0.25729084 0.28301992
[7] 0.31132191 0.34245411 0.37669952 0.39463759 0.37669952 0.34245411
[13] 0.31132191 0.28301992 0.25729084 0.23390076 0.21263706 0.19330642
[19] 0.18410135 0.19330642 0.21263706 0.23390076 0.25729084 0.28301992
[25] 0.31132191 0.34245411 0.37669952 0.39463759 0.37669952 0.34245411
[31] 0.31132191 0.28301992 0.25729084 0.23390076 0.21263706 0.19330642
[37] 0.09205067
$N
[1] 36
attr(,"class")
[1] "grid.1D"
$x.up
[1] 0
$x.down
[1] 10
$x.mid
[1] 0.1000059 0.3048835 0.5197296 0.7450293 0.9812912 1.2290485 1.4888608
[8] 1.7613145 2.0470246 2.3466363 2.6533637 2.9529754 3.2386855 3.5111392
[15] 3.7709515 4.0187088 4.2549707 4.4802704 4.6951165 4.8999941 5.1000025
[22] 5.3471071 5.7105939 6.2452773 7.0317879 7.9682121 8.7547227 9.2894061
[29] 9.6528929 9.8999975
$x.int
[1] 0.0000000 0.2000117 0.4097552 0.6297040 0.8603546 1.1022277
[7] 1.3558694 1.6218522 1.9007767 2.1932725 2.5000000 2.8067275
[13] 3.0992233 3.3781478 3.6441306 3.8977723 4.1396454 4.3702960
[19] 4.5902448 4.7999883 5.0000000 5.2000050 5.4942092 5.9269787
[25] 6.5635759 7.5000000 8.4364241 9.0730213 9.5057908 9.7999950
[31] 10.0000000
$dx
[1] 0.2000117 0.2097435 0.2199488 0.2306506 0.2418731 0.2536417 0.2659828
[8] 0.2789245 0.2924958 0.3067275 0.3067275 0.2924958 0.2789245 0.2659828
[15] 0.2536417 0.2418731 0.2306506 0.2199488 0.2097435 0.2000117 0.2000050
[22] 0.2942042 0.4327696 0.6365971 0.9364241 0.9364241 0.6365971 0.4327696
[29] 0.2942042 0.2000050
$dx.aux
[1] 0.1000059 0.2048776 0.2148461 0.2252997 0.2362618 0.2477574 0.2598123
[8] 0.2724537 0.2857102 0.2996116 0.3067275 0.2996116 0.2857102 0.2724537
[15] 0.2598123 0.2477574 0.2362618 0.2252997 0.2148461 0.2048776 0.2000084
[22] 0.2471046 0.3634869 0.5346834 0.7865106 0.9364241 0.7865106 0.5346834
[29] 0.3634869 0.2471046 0.1000025
$N
[1] 30
attr(,"class")
[1] "grid.1D"
ReacTran documentation built on Dec. 18, 2019, 3:12 a.m.
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Description Usage Arguments Value Author(s) See Also Examples
View source: R/setup.grid.1D.R
Description
Subdivides the one-dimensional model domain into one or more zones that
are each sub-divided into grid cells. The resulting grid structure can be
used in the other ReacTran functions.
The grid structure is characterized by the position of the middle of
the grid cells (x.mid) and the position of the interfaces between
grid cells (x.int).
Distances are calculated between the interfaces (dx), i.e. the
thickness of the grid cells. An auxiliary set of distances (dx.aux)
is calculated between the points where the concentrations are specified
(at the center of each grid cell and the two external interfaces).
A more complex grid consisting of multiple zones can be constructed when
specifying the endpoints of ech zone (x.down), the interval length
(L), and the number of layers in each zone (N) as vectors.
In each zone, one can control the grid resolution near the upstream and
downstream boundary.
The grid resolution at the upstream interface changes according to the
power law relation dx[i+1] = min(max.dx.1,p.dx.1*dx[i]),
where p.dx.1 determines the rate of increase and max.dx.1
puts an upper limit on the grid cell size.
A similar formula controls the resolution at the downstream interface. This allows refinement of the grid near the interfaces.
If only x.up, N and dx.1 are specified, then the grid size
is taken constant = dx.1 (and L=N*dx.1)
Usage
1 2 3 4 5 6 |
Arguments
x.up |
position of the upstream interface; one value [L] |
x.down |
position of the endpoint of each zone; one value when the
model domain covers only one zone ( |
L |
thickness of zones; one value (model domain = one zone) or a vector of length M (model domain = M zones) [L] |
N |
number of grid cells within a zone; one value or a vector of length M [-] |
dx.1 |
size of the first grid cell in a zone; one value or a vector of length M [L] |
p.dx.1 |
power factor controlling the increase in grid cell size near the upstream boundary; one value or a vector of length M. The default value is 1 (constant grid cell size) [-] |
max.dx.1 |
maximum grid cell size in the upstream half of the zone; one value or a vector of length M [L] |
dx.N |
size of the last grid cell in a zone; one value or a vector of length M [L] |
p.dx.N |
power factor controlling the increase in grid cell size near the downstream boundary; one value or a vector of length M. The default value is 1 (constant grid cell size) [-] |
max.dx.N |
maximum grid cell size in the downstream half of the zone; one value or a vector of length M [L] |
x |
the object of class |
... |
additional arguments passed to the function plot |
Value
a list of type grid.1D containing:
N |
the total number of grid cells [-] |
x.up |
position of the upstream interface; one value [L] |
x.down |
position of the downstream interface; one value [L] |
x.mid |
position of the middle of the grid cells;
vector of length |
x.int |
position of the interfaces of the grid cells;
vector of length |
dx |
distance between adjacent cell interfaces (thickness of grid
cells); vector of length |
dx.aux |
auxiliary vector containing the distance between adjacent
cell centers; at the upper and lower boundary calculated as
( |
Author(s)
Filip Meysman <filip.meysman@nioz.nl>, Karline Soetaert <karline.soetaert@nioz.nl>
See Also
tran.1D, for a discretisation of the general transport equation in 1-D
setup.grid.2D for the creation of grids in 2-D
setup.prop.1D, for defining properties on the 1-D grid.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 | # one zone, constant resolution
(GR <- setup.grid.1D(x.up = 0, L = 10, N = 10))
(GR <- setup.grid.1D(x.up = 0, L = 10, dx.1 = 1))
(GR <- setup.grid.1D(x.up = 0, L = 10, dx.N = 1))
plot(GR)
# one zone, constant resolution, origin not zero
(GR <- setup.grid.1D(x.up = 5, x.down = 10, N = 10))
plot(GR)
# one zone, variable resolution
(GR <- setup.grid.1D(x.up = 0, L = 10, dx.1 = 1, p.dx.1 = 1.2))
(GR <- setup.grid.1D(x.up = 0, L = 10, dx.N = 1, p.dx.N = 1.2))
plot(GR)
# one zone, variable resolution, imposed number of layers
(GR <- setup.grid.1D(x.up = 0, L = 10, N = 6, dx.1 = 1, p.dx.1 = 1.2))
(GR <- setup.grid.1D(x.up = 0, L = 10, N = 6, dx.N = 1, p.dx.N = 1.2))
plot(GR)
# one zone, higher resolution near upstream and downstream interfaces
(GR <- setup.grid.1D(x.up = 0, x.down = 10, dx.1 = 0.1,
p.dx.1 = 1.2, dx.N = 0.1, p.dx.N = 1.2))
plot(GR)
# one zone, higher resolution near upstream and downstream interfaces
# imposed number of layers
(GR <- setup.grid.1D(x.up = 0, x.down = 10, N = 20,
dx.1 = 0.1, p.dx.1 = 1.2,
dx.N = 0.1, p.dx.N = 1.2))
plot(GR)
# two zones, higher resolution near the upstream
# and downstream interface
(GR<-setup.grid.1D(x.up = 0, L = c(5, 5),
dx.1 = c(0.2, 0.2), p.dx.1 = c(1.1, 1.1),
dx.N = c(0.2, 0.2), p.dx.N = c(1.1, 1.1)))
plot(GR)
# two zones, higher resolution near the upstream
# and downstream interface
# the number of grid cells in each zone is imposed via N
(GR <- setup.grid.1D(x.up = 0, L = c(5, 5), N = c(20, 10),
dx.1 = c(0.2, 0.2), p.dx.1 = c(1.1, 1.1),
dx.N = c(0.2, 0.2), p.dx.N = c(1.1, 1.1)))
plot(GR)
|
Example output
Loading required package: rootSolve
Loading required package: deSolve
Loading required package: shape
$x.up
[1] 0
$x.down
[1] 10
$x.mid
[1] 0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5
$x.int
[1] 0 1 2 3 4 5 6 7 8 9 10
$dx
[1] 1 1 1 1 1 1 1 1 1 1
$dx.aux
[1] 0.5 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.5
$N
[1] 10
attr(,"class")
[1] "grid.1D"
$x.up
[1] 0
$x.down
[1] 10
$x.mid
[1] 0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5
$x.int
[1] 0 1 2 3 4 5 6 7 8 9 10
$dx
[1] 1 1 1 1 1 1 1 1 1 1
$dx.aux
[1] 0.5 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.5
$N
[1] 10
attr(,"class")
[1] "grid.1D"
$x.up
[1] 0
$x.down
[1] 10
$x.mid
[1] 0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5
$x.int
[1] 0 1 2 3 4 5 6 7 8 9 10
$dx
[1] 1 1 1 1 1 1 1 1 1 1
$dx.aux
[1] 0.5 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.5
$N
[1] 10
attr(,"class")
[1] "grid.1D"
$x.up
[1] 5
$x.down
[1] 10
$x.mid
[1] 5.25 5.75 6.25 6.75 7.25 7.75 8.25 8.75 9.25 9.75
$x.int
[1] 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0
$dx
[1] 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
$dx.aux
[1] 0.25 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.25
$N
[1] 10
attr(,"class")
[1] "grid.1D"
$x.up
[1] 0
$x.down
[1] 10
$x.mid
[1] 0.3871196 1.2387828 2.2607786 3.4871736 4.9588476 6.7248564 8.8440670
$x.int
[1] 0.0000000 0.7742393 1.7033264 2.8182309 4.1561164 5.7615789 7.6881339
[8] 10.0000000
$dx
[1] 0.7742393 0.9290871 1.1149045 1.3378854 1.6054625 1.9265550 2.3118661
$dx.aux
[1] 0.3871196 0.8516632 1.0219958 1.2263950 1.4716740 1.7660088 2.1192105
[8] 1.1559330
$N
[1] 7
attr(,"class")
[1] "grid.1D"
$x.up
[1] 0
$x.down
[1] 10
$x.mid
[1] 1.155933 3.275144 5.041152 6.512826 7.739221 8.761217 9.612880
$x.int
[1] 0.000000 2.311866 4.238421 5.843884 7.181769 8.296674 9.225761
[8] 10.000000
$dx
[1] 2.3118661 1.9265550 1.6054625 1.3378854 1.1149045 0.9290871 0.7742393
$dx.aux
[1] 1.1559330 2.1192105 1.7660088 1.4716740 1.2263950 1.0219958 0.8516632
[8] 0.3871196
$N
[1] 7
attr(,"class")
[1] "grid.1D"
$x.up
[1] 0
$x.down
[1] 10
$x.mid
[1] 0.5000011 1.6013999 2.9261544 4.5195596 6.4360959 8.7412919
$x.int
[1] 0.000000 1.000002 2.202798 3.649511 5.389608 7.482584 10.000000
$dx
[1] 1.000002 1.202795 1.446714 1.740097 2.092976 2.517416
$dx.aux
[1] 0.5000011 1.1013988 1.3247545 1.5934052 1.9165363 2.3051960 1.2587081
$N
[1] 6
attr(,"class")
[1] "grid.1D"
$x.up
[1] 0
$x.down
[1] 10
$x.mid
[1] 1.258708 3.563904 5.480440 7.073846 8.398600 9.499999
$x.int
[1] 0.000000 2.517416 4.610392 6.350489 7.797202 8.999998 10.000000
$dx
[1] 2.517416 2.092976 1.740097 1.446714 1.202795 1.000002
$dx.aux
[1] 1.2587081 2.3051960 1.9165363 1.5934052 1.3247545 1.1013988 0.5000011
$N
[1] 6
attr(,"class")
[1] "grid.1D"
$x.up
[1] 0
$x.down
[1] 10
$x.mid
[1] 0.04223264 0.13514444 0.24663861 0.38043160 0.54098320 0.73364512
[7] 0.96483942 1.24227258 1.57519237 1.97469612 2.45410062 3.02938601
[13] 3.71972849 4.54813947 5.45186053 6.28027151 6.97061399 7.54589938
[19] 8.02530388 8.42480763 8.75772742 9.03516058 9.26635488 9.45901680
[25] 9.61956840 9.75336139 9.86485556 9.95776736
$x.int
[1] 0.00000000 0.08446528 0.18582361 0.30745361 0.45340960 0.62855680
[7] 0.83873343 1.09094540 1.39359975 1.75678498 2.19260725 2.71559398
[13] 3.34317805 4.09627894 5.00000000 5.90372106 6.65682195 7.28440602
[19] 7.80739275 8.24321502 8.60640025 8.90905460 9.16126657 9.37144320
[25] 9.54659040 9.69254639 9.81417639 9.91553472 10.00000000
$dx
[1] 0.08446528 0.10135833 0.12163000 0.14595600 0.17514720 0.21017664
[7] 0.25221196 0.30265436 0.36318523 0.43582227 0.52298673 0.62758407
[13] 0.75310089 0.90372106 0.90372106 0.75310089 0.62758407 0.52298673
[19] 0.43582227 0.36318523 0.30265436 0.25221196 0.21017664 0.17514720
[25] 0.14595600 0.12163000 0.10135833 0.08446528
$dx.aux
[1] 0.04223264 0.09291180 0.11149416 0.13379300 0.16055160 0.19266192
[7] 0.23119430 0.27743316 0.33291979 0.39950375 0.47940450 0.57528540
[13] 0.69034248 0.82841097 0.90372106 0.82841097 0.69034248 0.57528540
[19] 0.47940450 0.39950375 0.33291979 0.27743316 0.23119430 0.19266192
[25] 0.16055160 0.13379300 0.11149416 0.09291180 0.04223264
$N
[1] 28
attr(,"class")
[1] "grid.1D"
$x.up
[1] 0
$x.down
[1] 10
$x.mid
[1] 0.04999958 0.16661030 0.32196303 0.52892919 0.80465650 1.17198974
[7] 1.66136350 2.31332376 3.18188725 4.33901687 5.66098313 6.81811275
[13] 7.68667624 8.33863650 8.82801026 9.19534350 9.47107081 9.67803697
[19] 9.83338970 9.95000042
$x.int
[1] 0.00000000 0.09999916 0.23322143 0.41070463 0.64715375 0.96215925
[7] 1.38182023 1.94090677 2.68574075 3.67803374 5.00000000 6.32196626
[13] 7.31425925 8.05909323 8.61817977 9.03784075 9.35284625 9.58929537
[19] 9.76677857 9.90000084 10.00000000
$dx
[1] 0.09999916 0.13322226 0.17748320 0.23644912 0.31500551 0.41966098
[7] 0.55908654 0.74483398 0.99229299 1.32196626 1.32196626 0.99229299
[13] 0.74483398 0.55908654 0.41966098 0.31500551 0.23644912 0.17748320
[19] 0.13322226 0.09999916
$dx.aux
[1] 0.04999958 0.11661071 0.15535273 0.20696616 0.27572731 0.36733324
[7] 0.48937376 0.65196026 0.86856349 1.15712963 1.32196626 1.15712963
[13] 0.86856349 0.65196026 0.48937376 0.36733324 0.27572731 0.20696616
[19] 0.15535273 0.11661071 0.04999958
$N
[1] 20
attr(,"class")
[1] "grid.1D"
$x.up
[1] 0
$x.down
[1] 10
$x.mid
[1] 0.09205067 0.28535709 0.49799415 0.73189491 0.98918575 1.27220567
[7] 1.58352758 1.92598169 2.30268121 2.69731879 3.07401831 3.41647242
[13] 3.72779433 4.01081425 4.26810509 4.50200585 4.71464291 4.90794933
[19] 5.09205067 5.28535709 5.49799415 5.73189491 5.98918575 6.27220567
[25] 6.58352758 6.92598169 7.30268121 7.69731879 8.07401831 8.41647242
[31] 8.72779433 9.01081425 9.26810509 9.50200585 9.71464291 9.90794933
$x.int
[1] 0.0000000 0.1841013 0.3866128 0.6093755 0.8544144 1.1239571
[7] 1.4204542 1.7466010 2.1053624 2.5000000 2.8946376 3.2533990
[13] 3.5795458 3.8760429 4.1455856 4.3906245 4.6133872 4.8158987
[19] 5.0000000 5.1841013 5.3866128 5.6093755 5.8544144 6.1239571
[25] 6.4204542 6.7466010 7.1053624 7.5000000 7.8946376 8.2533990
[31] 8.5795458 8.8760429 9.1455856 9.3906245 9.6133872 9.8158987
[37] 10.0000000
$dx
[1] 0.1841013 0.2025115 0.2227626 0.2450389 0.2695428 0.2964971 0.3261468
[8] 0.3587614 0.3946376 0.3946376 0.3587614 0.3261468 0.2964971 0.2695428
[15] 0.2450389 0.2227626 0.2025115 0.1841013 0.1841013 0.2025115 0.2227626
[22] 0.2450389 0.2695428 0.2964971 0.3261468 0.3587614 0.3946376 0.3946376
[29] 0.3587614 0.3261468 0.2964971 0.2695428 0.2450389 0.2227626 0.2025115
[36] 0.1841013
$dx.aux
[1] 0.09205067 0.19330642 0.21263706 0.23390076 0.25729084 0.28301992
[7] 0.31132191 0.34245411 0.37669952 0.39463759 0.37669952 0.34245411
[13] 0.31132191 0.28301992 0.25729084 0.23390076 0.21263706 0.19330642
[19] 0.18410135 0.19330642 0.21263706 0.23390076 0.25729084 0.28301992
[25] 0.31132191 0.34245411 0.37669952 0.39463759 0.37669952 0.34245411
[31] 0.31132191 0.28301992 0.25729084 0.23390076 0.21263706 0.19330642
[37] 0.09205067
$N
[1] 36
attr(,"class")
[1] "grid.1D"
$x.up
[1] 0
$x.down
[1] 10
$x.mid
[1] 0.1000059 0.3048835 0.5197296 0.7450293 0.9812912 1.2290485 1.4888608
[8] 1.7613145 2.0470246 2.3466363 2.6533637 2.9529754 3.2386855 3.5111392
[15] 3.7709515 4.0187088 4.2549707 4.4802704 4.6951165 4.8999941 5.1000025
[22] 5.3471071 5.7105939 6.2452773 7.0317879 7.9682121 8.7547227 9.2894061
[29] 9.6528929 9.8999975
$x.int
[1] 0.0000000 0.2000117 0.4097552 0.6297040 0.8603546 1.1022277
[7] 1.3558694 1.6218522 1.9007767 2.1932725 2.5000000 2.8067275
[13] 3.0992233 3.3781478 3.6441306 3.8977723 4.1396454 4.3702960
[19] 4.5902448 4.7999883 5.0000000 5.2000050 5.4942092 5.9269787
[25] 6.5635759 7.5000000 8.4364241 9.0730213 9.5057908 9.7999950
[31] 10.0000000
$dx
[1] 0.2000117 0.2097435 0.2199488 0.2306506 0.2418731 0.2536417 0.2659828
[8] 0.2789245 0.2924958 0.3067275 0.3067275 0.2924958 0.2789245 0.2659828
[15] 0.2536417 0.2418731 0.2306506 0.2199488 0.2097435 0.2000117 0.2000050
[22] 0.2942042 0.4327696 0.6365971 0.9364241 0.9364241 0.6365971 0.4327696
[29] 0.2942042 0.2000050
$dx.aux
[1] 0.1000059 0.2048776 0.2148461 0.2252997 0.2362618 0.2477574 0.2598123
[8] 0.2724537 0.2857102 0.2996116 0.3067275 0.2996116 0.2857102 0.2724537
[15] 0.2598123 0.2477574 0.2362618 0.2252997 0.2148461 0.2048776 0.2000084
[22] 0.2471046 0.3634869 0.5346834 0.7865106 0.9364241 0.7865106 0.5346834
[29] 0.3634869 0.2471046 0.1000025
$N
[1] 30
attr(,"class")
[1] "grid.1D"
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