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Merge pull request #134 from fverdugo/vanilla_amg
Add smoothed aggregation solver
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‎.github/workflows/ci.yml‎

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name: CI
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on:
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- push
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- pull_request
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push:
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branches:
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- main
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tags: '*'
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pull_request:
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concurrency:
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# Skip intermediate builds: always.
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# Cancel intermediate builds: only if it is a pull request build.
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group: ${{ github.workflow }}-${{ github.ref }}
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cancel-in-progress: ${{ startsWith(github.ref, 'refs/pull/') }}
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jobs:
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test:
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name: Julia ${{ matrix.version }} - ${{ matrix.os }} - ${{ matrix.arch }} - ${{ github.event_name }}
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name: PartitionedArrays / Julia ${{ matrix.version }} - ${{ matrix.os }} - ${{ matrix.arch }} - ${{ github.event_name }}
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runs-on: ${{ matrix.os }}
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strategy:
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fail-fast: false
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matrix:
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version:
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- '1.6'
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- '1' # Latest 1.X
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- '1'
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os:
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- ubuntu-latest
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arch:
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- uses: julia-actions/julia-buildpkg@v1
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- uses: julia-actions/julia-runtest@v1
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- uses: julia-actions/julia-processcoverage@v1
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- uses: codecov/codecov-action@v1
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- uses: codecov/codecov-action@v2
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with:
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file: lcov.info
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files: lcov.info
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PartitionedSolvers:
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name: PartitionedSolvers / Julia ${{ matrix.version }} - ${{ matrix.os }} - ${{ matrix.arch }} - ${{ github.event_name }}
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runs-on: ${{ matrix.os }}
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strategy:
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fail-fast: false
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matrix:
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version:
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- '1'
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os:
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- ubuntu-latest
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arch:
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- x64
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steps:
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- uses: actions/checkout@v2
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- uses: julia-actions/setup-julia@v1
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with:
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version: ${{ matrix.version }}
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arch: ${{ matrix.arch }}
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- uses: julia-actions/cache@v1
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- uses: julia-actions/julia-buildpkg@v1
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- run: |
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julia --project=extensions/PartitionedSolvers -e '
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using Pkg
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Pkg.develop(path=".")
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Pkg.test("PartitionedSolvers")'
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docs:
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name: Documentation
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runs-on: ubuntu-latest
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permissions:
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contents: write
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steps:
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- uses: actions/checkout@v2
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- uses: julia-actions/setup-julia@v1
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with:
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version: '1'
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- uses: julia-actions/cache@v1
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- name: Install dependencies
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run: julia --project=docs -e 'using Pkg; Pkg.instantiate()'
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- name: Build and deploy
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- uses: julia-actions/julia-buildpkg@v1
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- run: |
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julia --project=docs -e '
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using Pkg
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Pkg.develop(path="extensions/PartitionedSolvers")'
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- uses: julia-actions/julia-docdeploy@v1
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env:
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GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}
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DOCUMENTER_KEY: ${{ secrets.DOCUMENTER_KEY }}
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run: julia --project=docs docs/make.jl
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- run: |
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julia --project=docs -e '
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using Documenter: DocMeta, doctest
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using PartitionedArrays
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DocMeta.setdocmeta!(PartitionedArrays, :DocTestSetup, :(using PartitionedArrays); recursive=true)
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doctest(PartitionedArrays)'

‎docs/Manifest.toml‎

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julia_version = "1.10.0"
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manifest_format = "2.0"
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project_hash = "e37729e95710f39fa1cd840707ef95d2e3bbf22c"
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project_hash = "6cb04e0444d1618368044337280d73d6270dffbd"
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[[deps.ANSIColoredPrinters]]
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git-tree-sha1 = "574baf8110975760d391c710b6341da1afa48d8c"
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deps = ["CircularArrays", "Distances", "FillArrays", "IterativeSolvers", "LinearAlgebra", "MPI", "Printf", "Random", "SparseArrays", "SparseMatricesCSR"]
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path = ".."
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uuid = "5a9dfac6-5c52-46f7-8278-5e2210713be9"
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version = "0.3.4"
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version = "0.4.3"
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[[deps.PartitionedSolvers]]
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deps = ["IterativeSolvers", "LinearAlgebra", "PartitionedArrays", "Random", "SparseArrays"]
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path = "../extensions/PartitionedSolvers"
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uuid = "11b65f7f-80ac-401b-9ef2-3db765482d62"
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version = "0.1.0"
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[[deps.Pkg]]
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deps = ["Artifacts", "Dates", "Downloads", "FileWatching", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "Serialization", "TOML", "Tar", "UUIDs", "p7zip_jll"]

‎docs/Project.toml‎

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IterativeSolvers = "42fd0dbc-a981-5370-80f2-aaf504508153"
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Literate = "98b081ad-f1c9-55d3-8b20-4c87d4299306"
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PartitionedArrays = "5a9dfac6-5c52-46f7-8278-5e2210713be9"
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PartitionedSolvers = "11b65f7f-80ac-401b-9ef2-3db765482d62"

‎docs/examples.jl‎

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r = A*x - b
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norm(r)
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# # Distributed algebraic multigrid (AMG)
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#
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# So far, we have use a conjugate gradient method to solve the linear system. However, this is approach does not scale well
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# to larger problems and one needs to consider a preconditioner. A distributed algebraic multigrid (AMG) preconditioner is available in `PartitonedSolvers`, an extension
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# package of `PartitionedArrays` that provides parallel solvers for systems built with matrices and vectors from `PartitionedArrays`.
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#
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# First, let us solve a larger problem without a preconditioner. To this end we use function `laplace_matrix` that builds a Laplace matrix of
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# arbitrary size.
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using PartitionedArrays: laplace_matrix
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nodes_per_dir = (40,40,40)
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parts_per_dir = (2,2,1)
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nparts = prod(parts_per_dir)
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parts = LinearIndices((nparts,))
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A = laplace_matrix(nodes_per_dir,parts_per_dir,parts)
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x_exact = pones(partition(axes(A,2)))
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b = A*x_exact
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# Now, we have a matrix and a rhs vector. Let us solve the system:
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x = similar(b,axes(A,2))
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x .= 0
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_, history = IterativeSolvers.cg!(x,A,b;log=true)
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history
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# Now solve the system while using an AMG preconditioner.
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using PartitionedSolvers: amg, preconditioner
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x .= 0
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Pl = preconditioner(amg(),x,A,b)
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_, history = IterativeSolvers.cg!(x,A,b;Pl,log=true)
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history
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‎extensions/PartitionedSolvers/Project.toml‎

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name = "PartitionedSolvers"
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uuid = "11b65f7f-80ac-401b-9ef2-3db765482d62"
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authors = ["Francesc Verdugo <f.verdugo.rojano@vu.nl>"]
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version = "0.1.0"
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[deps]
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IterativeSolvers = "42fd0dbc-a981-5370-80f2-aaf504508153"
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LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
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PartitionedArrays = "5a9dfac6-5c52-46f7-8278-5e2210713be9"
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Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
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SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
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[extras]
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Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
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[targets]
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test = ["Test"]

‎extensions/PartitionedSolvers/src/PartitionedSolvers.jl‎

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module PartitionedSolvers
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using PartitionedArrays
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using SparseArrays
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using LinearAlgebra
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export setup
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export solve!
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export setup!
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export finalize!
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export AbstractLinearSolver
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export linear_solver
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export attach_nullspace
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export default_nullspace
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export preconditioner
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export matrix
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export nullspace
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include("interfaces.jl")
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export lu_solver
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export jacobi_correction
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export richardson
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export jacobi
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export gauss_seidel
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export additive_schwarz_correction
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export additive_schwarz
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include("smoothers.jl")
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export amg
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export smoothed_aggregation
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export v_cycle
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export w_cycle
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export amg_level_params
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export amg_fine_params
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export amg_coarse_params
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export amg_statistics
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include("amg.jl")
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end # module

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