Performance issues with parallel Julia code - performance

Question

I am working on a scientific code that is experiencing issues with parallelization.
The parallel version is slower than the serial one and I am not sure if the right approaches are used for this application.
How can I improve the performance of the parallel calculation?
Is the right approach being used or should other packages / functions be considered for parallelization?
I have already tried a larger workload, however this makes no difference.
I suspect the problem is somehow due to data movement between workers, but I don't know how to check or improve this one.
Parallel programming with Julia is still relatively new for me, so I am very grateful for any help!
The simulation code is something of a benchmark for the Julia programming language, as our team is considering using Julia for all future projects if strong performance advantages to the current workflow can be demonstrated.
Because of this, I would like to maximize performance, also since calculations with very large models as well as possible use on a cluster are planned.
Minimum Working Example
The critical parts of the code can be broken down to the following example.
I start the process as follows:
using Distributed
addprocs();
#everywhere using SharedArrays, LinearAlgebra, Test
First I define the simulation model, containing all data used for the calculations.
Is it actually okay to store SharedArrays with other data in a struct or should a different approach be used?
#everywhere struct Model
idx::Vector{Tuple{Int,Int}} # indices
A::SharedMatrix{Float64} # results, will be constantly updated
B::Vector{Float64} # part of pre-processing, will only be read
end
See the non-parallel version of the function used for the update of the model below.
function update(m::Model, factor::Float64)
L::Float64 = 0.
k::Float64 = 0.
cnt::Int = 0
for (i,j) in m.idx
cnt+=1
L = norm(m.A[:,i]-m.A[:,j])
k = factor * m.B[cnt]
m.A[:,i] .+= k*L
m.A[:,j] .-= k*L
end
end
For parallelization, I simply tried the following. Is perhaps an approach with pmap better in this case?
#everywhere function parallel_update(m::Model, factor::Float64)
L::Float64 = 0.
k::Float64 = 0.
cnt::Int = 0
#sync #distributed for (i,j) in m.idx
cnt+=1
L = norm(m.A[:,i]-m.A[:,j])
k = factor * m.B[cnt]
m.A[:,i] .+= k*L
m.A[:,j] .-= k*L
end
end
To test the results I use the following function:
#everywhere function test_my_code()
# provide some data
n = 10000000
idx = [(rand(1:n),rand(1:n)) for k=1:n]
A = SharedArray(hcat(([rand(0.:1000.);rand(0.:1000.);rand(0.:1000.)] for k=1:n)...))
B = [rand(0.:1000.) for k=1:n]
# define models
model1 = Model(idx,A,B)
model2 = Model(idx,A,B)
# test and compare results
#time update(model1,2.)
#time parallel_update(model2,2.)
#test model1 == model2
end
julia> test_my_code() # first run
6.350694 seconds (50.00 M allocations: 5.215 GiB, 13.66% gc time)
11.422999 seconds (6.69 k allocations: 446.156 KiB)
Test Passed
julia> test_my_code() # second run
6.286828 seconds (50.00 M allocations: 5.215 GiB, 18.35% gc time)
6.297144 seconds (2.92 k allocations: 143.516 KiB)
Test Passed
Note: significant performance improvements for the serial code
I was already able to significantly improve the performance of the serial function and reduce the number of allocations to zero.
Since this seems to make no difference to the parallelization problem, I used the shorter, easier-to-read version for the previous example.
See the serial code below.
using LinearAlgebra, Test
struct Model
idx::Vector{Tuple{Int,Int}}
A::Matrix{Float64}
B::Vector{Float64}
end
function update(m::Model, factor::Float64)
L::Float64 = 0.
k::Float64 = 0.
cnt::Int = 0
for (i,j) in m.idx
cnt+=1
L = norm(m.A[:,i]-m.A[:,j])
k = factor * m.B[cnt]
m.A[:,i] .+= k*L
m.A[:,j] .-= k*L
end
end
function update_fast(m::Model, factor::Float64)
L::Float64 = 0.
k::Float64 = 0.
cnt::Int = 0
for (i,j) in m.idx
cnt+=1
L = sqrt((m.A[1,i]-m.A[1,j])^2 +
(m.A[2,i]-m.A[2,j])^2 +
(m.A[3,i]-m.A[3,j])^2)
k = factor * m.B[cnt]
m.A[1,i] += k*L
m.A[2,i] += k*L
m.A[3,i] += k*L
m.A[1,j] -= k*L
m.A[2,j] -= k*L
m.A[3,j] -= k*L
end
end
function test_serial_speedup()
n = 10000000
idx = [(rand(1:n),rand(1:n)) for k=1:n]
A = hcat(([rand(0.:1000.);rand(0.:1000.);rand(0.:1000.)] for k=1:n)...)
B = [rand(0.:1000.) for k=1:n]
model1 = Model(idx,A,B)
model2 = Model(idx,A,B)
#time update(model1,2.)
#time update_fast(model2,2.)
#test model1 == model2
end
julia> test_serial_speedup()
5.008049 seconds (50.00 M allocations: 5.215 GiB, 18.14% gc time)
0.464986 seconds
Test Passed