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Adi2D_Ref

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This commit is contained in:
Marco De Lucia 2023-03-17 10:57:07 +01:00
parent e4ec0a11da
commit cea941853b
1 changed files with 17 additions and 9 deletions
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26
scripts/Adi2D_Reference.R
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@ -1,4 +1,4 @@
## Time-stamp: "Last modified 2022-12-21 18:47:13 delucia"
## Time-stamp: "Last modified 2023-01-05 17:52:55 delucia"
## Brutal implementation of 2D ADI scheme
## Square NxN grid with dx=dy=1
@ -272,8 +272,8 @@ ADIHetDir <- function(field, dt, iter, alpha) {
for (it in seq(1, iter)) {
for (i in seq(2, ny-1)) {
Aij <- cbind((alpha[i,]+alpha[i-1,])/2, (alpha[i,]+alpha[i+1,])/2)
Bij <- cbind((alpha[,i]+alpha[,i-1])/2, (alpha[,i]+alpha[,i+1])/2)
Aij <- cbind(harm(alpha[i,], alpha[i-1,]), harm(alpha[i,], alpha[i+1,]))
Bij <- cbind(harm(alpha[,i], alpha[,i-1]), harm(alpha[,i], alpha[,i+1]))
tmpX[i,] <- SweepByRowHetDir(i, res, dt=dt, Aij, Bij)
}
resY <- t(tmpX)
@ -286,6 +286,10 @@ ADIHetDir <- function(field, dt, iter, alpha) {
return(out)
}
harm <- function(x,y) 1/(1/x+1/y)
harm(1,4)
## Direct discretization, Workhorse function to fill A, B and solve
## for a given *row* of the grid matrix
@ -299,15 +303,17 @@ SweepByRowHetDir <- function(i, field, dt, Aij, Bij) {
## adjacent diagonals "Sx"
for (ii in seq(1, nrow(field)-1)) {
A[ii+1, ii] <- -Sx*Aij[ii,1]
A[ii, ii+1] <- -Sx*Aij[ii,2]
A[ii+1, ii] <- -Sx*Aij[ii,2] # i-1/2
A[ii, ii+1] <- -Sx*Aij[ii,1] # i+1/2
}
B <- numeric(ncol(field))
for (ii in seq_along(B))
B[ii] <- Sy*Bij[ii,2]*field[i+1,ii] + (1 - Sy*(Bij[ii,1]+Bij[ii,2]))*field[i, ii] + Sy*Bij[ii,1]*field[i-1,ii]
lastA <<- A
lastB <<- B
x <- solve(A, B)
x
}
@ -315,11 +321,11 @@ SweepByRowHetDir <- function(i, field, dt, Aij, Bij) {
## adi2 <- ADI(n=51, dt=10, iter=200, alpha=1E-3)
## ref2 <- DoRef(n=51, alpha=1E-3, dt=10, iter=200)
n <- 51
n <- 5
field <- matrix(0, n, n)
alphas <- matrix(1E-3*runif(n*n, 1,1.2), n, n)
alphas <- matrix(1E-5*runif(n*n, 1,2), n, n)
alphas1 <- matrix(1E-5, n, 25)
alphas1 <- matrix(3E-5, n, 25)
alphas2 <- matrix(1E-5, n, 26)
alphas <- cbind(alphas1, alphas2)
@ -352,3 +358,5 @@ image(alphas)
points(0.5,0.5, col="red",pch=4)
image(adih[[length(adih)]])
points(0.5,0.5, col="red",pch=4)
options(width=110)