max/tug
1
0
Fork 0
mirror of https://git.gfz-potsdam.de/naaice/tug.git synced 2025-12-13 09:28:23 +01:00
Code Issues Packages Projects Releases Wiki Activity

Small fixes

Browse Source
This commit is contained in:
Marco De Lucia 2022-12-21 18:54:15 +01:00
parent 7bd40639d5
commit 9815ebce9c
3 changed files with 15 additions and 9 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

1
.gitignore vendored
View File

@ -8,3 +8,4 @@ compile_commands.json
.cache/
.ccls-cache/
/iwyu/
.Rhistory

8
doc/ADI_scheme.org
View File

@ -419,8 +419,8 @@ approximation of $\frac{\partial}{\partial x} \left(\alpha(x)
\begin{aligned}
\frac{C^{t+1/2}_{i,j}-C^{t }_{i,j}}{\Delta t/2} = & \frac{1}{\Delta x^2} \left[ \alpha_{i+1/2,j} C^{t+1/2}_{i+1,j} - (\alpha_{i+1/2,j}+\alpha_{i-1/2,j}) C^{t+1/2}_{i,j} + \alpha_{i-1/2,j} C^{t+1/2}_{i-1,j}\right] + \\
& \frac{1}{\Delta y^2} \left[ \alpha_{i,j+1/2}C^{t}_{i,j+1} - (\alpha_{i,j+1/2}+\alpha_{i,j-1/2}) C^t_{i} + \alpha_{i,j-1/2}C^{t}_{i,j-1}\right]\\
\frac{C^{t+1 }_{i,j}-C^{t+1/2}_{i,j}}{\Delta t/2} = & \frac{1}{\Delta x^2} \left[ \alpha_{i+1/2,j}C^{t+1/2}_{i+1,j} - (\alpha_{i+1/2,j}+\alpha_{i-1/2,j}) C_{i} + \alpha_{i-1/2,j}C^{t+1/2}_{i-1,j}\right] + \\
& \frac{1}{\Delta y^2} \left[ \alpha_{i,j+1/2}C^{t+1}_{i,j+1} - (\alpha_{i,j+1/2}+\alpha_{i,j-1/2}) C^{t+1}_{i,j} + \alpha_{i,j-1/2}C^{t+1}_{i,j-1}\right]
\frac{C^{t+1 }_{i,j}-C^{t+1/2}_{i,j}}{\Delta t/2} = & \frac{1}{\Delta y^2} \left[ \alpha_{i+1/2,j}C^{t+1/2}_{i+1,j} - (\alpha_{i+1/2,j}+\alpha_{i-1/2,j}) C_{i} + \alpha_{i-1/2,j}C^{t+1/2}_{i-1,j}\right] + \\
& \frac{1}{\Delta x^2} \left[ \alpha_{i,j+1/2}C^{t+1}_{i,j+1} - (\alpha_{i,j+1/2}+\alpha_{i,j-1/2}) C^{t+1}_{i,j} + \alpha_{i,j-1/2}C^{t+1}_{i,j-1}\right]
\end{aligned}
\right.
\end{equation}
@ -432,9 +432,9 @@ explicit terms, the two sweeps become:
\begin{equation}
\left\{
\begin{aligned}
-S_x \alpha^x_{i+1/2,j} C^{t+1/2}_{i+1,j} + (1 + S_x(\alpha^x_{i+1/2,j}+ \alpha^x_{i-1/2,j}))C^{t+1/2}_{i,j} - S_x \alpha^x_{i-1/2,j} C^{t+1/2}_{i-1,j} = & \\
-S_x \alpha^x_{i+1/2,j} C^{t+1/2}_{i+1,j} + (1 + S_x(\alpha^x_{i+1/2,j}+ \alpha^x_{i-1/2,j}))C^{t+1/2}_{i,j} - S_x \alpha^x_{i-1/2,j} C^{t+1/2}_{i-1,j} = \quad & \\
S_y \alpha^y_{i,j+1/2} C^{t }_{i,j+1} + (1 - S_y(\alpha^y_{i,j+1/2}+ \alpha^y_{i,j-1/2}))C^{t }_{i,j} + S_y \alpha^y_{i,j-1/2} C^{t }_{i,j-1} & \\[1em]
-S_y \alpha^y_{i,j+1/2} C^{t+1 }_{i,j+1} + (1 + S_y(\alpha^y_{i,j+1/2}+ \alpha^y_{i,j-1/2}))C^{t+1 }_{i,j} - S_y \alpha^y_{i,j-1/2} C^{t+1 }_{i,j-1} = & \\
-S_y \alpha^y_{i,j+1/2} C^{t+1 }_{i,j+1} + (1 + S_y(\alpha^y_{i,j+1/2}+ \alpha^y_{i,j-1/2}))C^{t+1 }_{i,j} - S_y \alpha^y_{i,j-1/2} C^{t+1 }_{i,j-1} = \qquad & \\
S_x \alpha^x_{i+1/2,j} C^{t+1/2}_{i+1,j} + (1 - S_x(\alpha^x_{i+1/2,j}+ \alpha^x_{i-1/2,j}))C^{t+1/2}_{i,j} + S_x \alpha^x_{i-1/2,j} C^{t+1/2}_{i-1,j}
\end{aligned}
\right.

15
scripts/Adi2D_Reference.R
View File

@ -1,4 +1,4 @@
## Time-stamp: "Last modified 2022-12-21 13:47:00 delucia"
## Time-stamp: "Last modified 2022-12-21 18:47:13 delucia"
## Brutal implementation of 2D ADI scheme
## Square NxN grid with dx=dy=1
@ -319,21 +319,25 @@ n <- 51
field <- matrix(0, n, n)
alphas <- matrix(1E-3*runif(n*n, 1,1.2), n, n)
alphas1 <- matrix(1E-5, n, 25)
alphas2 <- matrix(1E-5, n, 26)
alphas <- cbind(alphas1, alphas2)
## for (i in seq(1,nrow(alphas)))
## alphas[i,] <- seq(1E-7,1E-3, length=n)
#diag(alphas) <- rep(1E-2, n)
adih <- ADIHetDir(field=field, dt=10, iter=100, alpha=alphas)
adi2 <- ADI(n=n, dt=10, iter=100, alpha=1E-3)
adih <- ADIHetDir(field=field, dt=10, iter=200, alpha=alphas)
adi2 <- ADI(n=n, dt=10, iter=200, alpha=1E-5)
par(mfrow=c(1,3))
image(adi2[[length(adi2)]])
image(adih[[length(adih)]])
points(0.5,0.5, col="red",pch=4)
plot(adih1[[length(adih1)]], adi2[[length(adi2)]], pch=4, log="xy")
plot(adih[[length(adih)]], adi2[[length(adi2)]], pch=4, log="xy")
abline(0,1)
@ -345,5 +349,6 @@ adi2
par(mfrow=c(1,2))
image(alphas)
image(adih1[[length(adih1)]])
points(0.5,0.5, col="red",pch=4)
image(adih[[length(adih)]])
points(0.5,0.5, col="red",pch=4)