Julia Parallel Distributed - parallel-processing

Question

I'm trying to run this code, but why I'm I getting these 2 rows in the Middle with 00000, can someone help me, to get that fixed, please?
using Distributed #Bereitstellung der Bibliothekee zur Parallelen Programieru
addprocs(2)
#everywhere using LinearAlgebra #Bereitstellung der LinearAlgebra Bibliotheke
#everywhere using DistributedArrays #Bereitstellung der DistributedArrays
#everywhere T =(zeros(n,n))
T[:,1].=10 #Randbedingungen T_links =10
T[:,end].=10 #Randbedingungen T_rechts =10
T = distribute(T; dist=(2,1))
#everywhere maxit = 100 #maximale Iterrationsanzahl
#everywhere function Poissons_2D(T)
for w in 1:maxit
#sync #distributed for p in 1:nworkers()
for i in 2:length(localindices(T)[1])-1
for j in 2:length(localindices(T)[2])-1
localpart(T)[i,j] = (1/4 * (localpart(T)[i-1,j] + localpart(T)[i+1,j] + localpart(T)[i,j-1] + localpart(T)[i,j+1]))
end
end
end
end
return T
end
Poissons_2D(T)
10×10 DArray{Float64,2,Array{Float64,2}}:
10.0 0.0 0.0 0.0 … 0.0 0.0 0.0 10.0
10.0 4.33779 2.00971 1.01077 1.01077 2.00971 4.33779 10.0
10.0 5.34146 2.69026 1.40017 1.40017 2.69026 5.34146 10.0
10.0 4.33779 2.00971 1.01077 1.01077 2.00971 4.33779 10.0
10.0 0.0 0.0 0.0 0.0 0.0 0.0 10.0
10.0 0.0 0.0 0.0 … 0.0 0.0 0.0 10.0
10.0 4.33779 2.00971 1.01077 1.01077 2.00971 4.33779 10.0
10.0 5.34146 2.69026 1.40017 1.40017 2.69026 5.34146 10.0
10.0 4.33779 2.00971 1.01077 1.01077 2.00971 4.33779 10.0
10.0 0.0 0.0 0.0 0.0 0.0 0.0 10.0

Answer 1

The first cleanup could look like this:
a =(zeros(10,10))
a[:,[1,end]] .= 10
a = distribute(a; dist=(nworkers(),1))
function Poissons_2D(a::DArray, maxit::Int=100)
for w in 1:maxit
#sync #distributed for p in 1:nworkers()
local_a = localpart(a)
local_ind = localindices(a)
for iix in 1:length(local_ind[1])
i = local_ind[1][iix]
(i==1 || i==size(a,1)) && continue
for j in local_ind[2][2:end-1]
local_a[iix,j] = (1/4 * (a[i-1,j] + a[i+1,j] + a[i,j-1] + a[i,j+1]))
end
end
end
end
a
end
Some remarks:
Do not use #everywhere in front of T - you do not want to define it on all workers
in Julia you use by convention T to denote parametric types so use a, or some T-like LaTeX symbol
However, your function takes values from all adjacent cells to calculate new values.
I do not know how do you plan to handle situation when the value does not exist yet.
In particular if each row requires value from the previous row and previous column it is not possible to parallelize this computation at all (because you need to wait for the previous value to get the next one).
julia> Poissons_2D(a)
10×10 DArray{Float64,2,Array{Float64,2}}:
10.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 10.0
10.0 4.99998 3.05213 2.20861 1.87565 1.87565 2.20862 3.05214 4.99999 10.0
10.0 6.9478 4.99994 3.90669 3.41834 3.41834 3.9067 4.99995 6.94781 10.0
10.0 7.7913 6.09315 4.99989 4.47269 4.4727 4.99991 6.09317 7.79131 10.0
10.0 8.12425 6.58148 5.52707 4.99987 4.99988 5.52709 6.58151 8.12427 10.0
10.0 8.12425 6.58148 5.52707 4.99987 4.99988 5.52709 6.58151 8.12427 10.0
10.0 7.7913 6.09316 4.99991 4.47271 4.47271 4.99992 6.09317 7.79131 10.0
10.0 6.94781 4.99995 3.90671 3.41835 3.41836 3.90672 4.99996 6.94782 10.0
10.0 4.99999 3.05214 2.20862 1.87566 1.87566 2.20863 3.05215 4.99999 10.0
10.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 10.0

Answer 2

I think the problem are the ranges of for with I and j. You range is from 2 to N-1, avoiding the extremes. It is right because you are missing the information to calculate them, because it is stored in a different process. However you need to transfer the limits information. In MPI, for instance you could send redundant information to avoid that, but in Distributed I am not sure. I see the cause, but the solution is not easy. At least I hope to have helped a little.