# Dividing a 1D domain into subdomains using Distributed Arrays (boundary element implementation)

**URL:** <https://discourse.julialang.org/t/dividing-a-1d-domain-into-subdomains-using-distributed-arrays-boundary-element-implementation/61858>\
**Category:** New to Julia\
**Tags:** distributed\
**Created:** [May 26, 2021, 1:55pm UTC](https://discourse.julialang.org/t/dividing-a-1d-domain-into-subdomains-using-distributed-arrays-boundary-element-implementation/61858 "2021-05-26T13:55:42Z")\
**Posts on this page:** 2\
**Page:** 1

<div class="post-metadata">

**Author:** ![Debasish](https://avatars.discourse-cdn.com/v4/letter/d/77aa72/32.png) [@Debasish](https://discourse.julialang.org/u/Debasish)\
**Post date:** [May 26, 2021, 1:55pm UTC](https://discourse.julialang.org/t/dividing-a-1d-domain-into-subdomains-using-distributed-arrays-boundary-element-implementation/61858/1 "2021-05-26T13:55:42Z")

</div>

Hello everyone,

I am new to Julia and this is a baby-step towards writing boundary element simulations with distributed computing.

I wish to divide a 1-D line (a sin-curve) into different domains (elements) and distributed them using @DArrays.  
**Question1** : I don’t understand how does the `I->fill` syntax below works. The result looks intuitive but I am not entirely sure how the code knows what values of ‘I’ to pick.

```julia
using Distributed, DistributedArrays, InteractiveUtils

# Add 4 processors only once
if nprocs() == 1
     addprocs(4)
else
     println("Only add 4 processors")
end

@everywhere using Distributed, DistributedArrays, InteractiveUtils

npts = 17
nelm = npts - 1
x = DArray(I->fill(myid(), length.(I)), (1, nelm), workers()[1:nworkers()], [1,nworkers()])

```

```julia
julia> x
1×16 DArray{Int64, 2, Matrix{Int64}}:
 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5

```

This is also related to the `I` that appears in the life-cellular automaton-example [Introduction · DistributedArrays.jl](https://juliaparallel.github.io/DistributedArrays.jl/dev/#Distributed-Array-Operations-1)  
I don’t understand how does the code know what values of I it needs to iterate in `DArray(size(d),procs(d)) do I `

**Question 2)** How do I implement the following two methods using @DArrays?

The sin curve

```julia
x = LinRange(-π,π,npts)

```

is discretized as

```julia
17-element LinRange{Float64}:
 -3.14159,-2.74889,-2.35619,-1.9635,-1.5708,-1.1781,-0.785398,-0.392699,0.0,0.392699,0.785398,1.1781,1.5708,1.9635,2.35619,2.74889,3.14159

```

which I wish to store in 4 processors as

Method-1 (store 4 elements in each processor)  
4 elements in Proc 1 → -3.14159, -2.74889, -2.356190, -1.963500, -1.5708  
4 elements in Proc 2 → -1.57080, -1.17810, -0.785398, -0.392699, 0.0  
4 elements in Proc 3 → 0.0, 0.392699, 0.785398, 1.1781, 1.5708  
4 elements in Proc 4 → 1.5708,1.9635,2.35619,2.74889,3.14159

As I store 4 elements in each processor I don’t need communication with others when I want to find properties of an element like normal vector etc.

Method - 2 (store 4 nodes in each processor)  
4 nodes in Proc 1 → -3.14159, -2.74889, -2.356190, -1.963500  
4 nodes in Proc 2 → -1.57080, -1.17810, -0.785398, -0.392699  
4 nodes in Proc 3 → 0.0, 0.392699, 0.785398, 1.1781  
4 nodes in Proc 4 → 1.5708,1.9635,2.35619,2.74889,3.14159

Here I don’t store the end nodes twice and some communication will be required when computing element properties. Method-2 is similar to the life-cellular automaton-example in the documentation of @DistributedArrays.jl

Any help is greatly appreciated. Thank you.

---

<div class="post-metadata">

**Author:** ![Debasish](https://avatars.discourse-cdn.com/v4/letter/d/77aa72/32.png) [@Debasish](https://discourse.julialang.org/u/Debasish)\
**Post date:** [May 27, 2021, 12:05pm UTC](https://discourse.julialang.org/t/dividing-a-1d-domain-into-subdomains-using-distributed-arrays-boundary-element-implementation/61858/2 "2021-05-27T12:05:09Z")

</div>

I have gotten it to work but it may not be written in the most elegant way as I am relatively new to Julia (\< 1 month old). I still don’t understand how to initialize such arrays using ` dfill(v, args...) = DArray(I->fill(v, map(length,I)), args...)` or lines such as ` DArray(size(d),procs(d)) do I`. It is not clear to me how how `I` values are picked  
[https://juliaparallel.github.io/DistributedArrays.jl/stable/#Distributed-Array-Operations-1](https://juliaparallel.github.io/DistributedArrays.jl/stable/#Distributed-Array-Operations-1)

If someone can comment on any better way to do this, I will be grateful.

```julia
using Distributed, DistributedArrays, InteractiveUtils, LinearAlgebra

# Add 4 processors only once
if nprocs() == 1
     addprocs(4)
else
     println("Only add 4 processors")
end

@everywhere using Distributed, DistributedArrays, InteractiveUtils, LinearAlgebra

npts = 16
# Method 1
x1 = Array{Float64}(undef, (npts,1))
x1[:,1] = -π:2π/(npts-1):π

# Remember p goes from 2 to 5 and not 1 to 4
xsplit = [@spawnat p x1[4p-7:4p-4] for p in workers()[1:4]]
D1 = DArray(xsplit)

# Method 2
x2 = Array{Float64}(undef, (npts+1,1))
x2[:,1] = -π:2π/npts:π
# Remember p goes from 2 to 5 and not 1 to 4
xsplit2 = [@spawnat p x2[4p-7:4p-3] for p in workers()[1:4]]
D2 = DArray(xsplit2)

```