JOSS paper

.github/workflows/joss.yml

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+name: Joss Paper
+on: [push]
+
+jobs:
+  paper:
+    runs-on: ubuntu-latest
+    name: Paper Draft Compilation
+    steps:
+      - name: Checkout
+        uses: actions/checkout@v4
+      - name: Build draft PDF
+        uses: openjournals/openjournals-draft-action@master
+        with:
+          journal: joss
+          # This should be the path to the paper within your repo.
+          paper-path: joss_paper/paper.md
+      - name: Upload
+        uses: actions/upload-artifact@v4
+        with:
+          name: paper
+          # This is the output path where Pandoc will write the compiled
+          # PDF. Note, this should be the same directory as the input
+          # paper.md
+          path: joss_paper/paper.pdf

.gitignore

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 .vscode
 Manifest.toml
 LocalPreferences.toml
-data
+data/*

joss_paper/.gitignore

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+paper.crossref
+paper.pdf
+demo

joss_paper/demo.jl

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+using Gridap, Gridap.Algebra, Gridap.MultiField
+using PartitionedArrays, GridapDistributed, GridapSolvers
+
+using GridapSolvers.LinearSolvers
+using GridapSolvers.MultilevelTools
+using GridapSolvers.BlockSolvers
+
+function get_bilinear_form(mh_lev,biform,qdegree)
+  model = get_model(mh_lev)
+  Ω = Triangulation(model)
+  dΩ = Measure(Ω,qdegree)
+  return (u,v) -> biform(u,v,dΩ)
+end
+
+function add_labels!(labels)
+  add_tag_from_tags!(labels,"top",[6])
+  add_tag_from_tags!(labels,"walls",[1,2,3,4,5,7,8])
+end
+
+with_mpi() do distribute
+  np_per_level = [(2,2),(1,1)] # Number of processors per GMG level
+  parts = distribute(LinearIndices((prod(np_per_level[1]),)))
+
+  # Create multi-level mesh
+  domain = (0,1,0,1) # Cartesian domain (xmin,xmax,ymin,ymax)
+  ncells = (10,10)   # Number of cells
+  mh = CartesianModelHierarchy(parts,np_per_level,domain,ncells;add_labels!)
+  model = get_model(mh,1) # Finest mesh
+
+  # Create FESpaces
+  fe_order = 2
+  reffe_u = ReferenceFE(lagrangian,VectorValue{2,Float64},fe_order)
+  reffe_p = ReferenceFE(lagrangian,Float64,fe_order-1;space=:P)
+
+  tests_u  = TestFESpace(mh,reffe_u,dirichlet_tags=["walls","top"])
+  trials_u = TrialFESpace(tests_u,[VectorValue(0.0,0.0),VectorValue(1.0,0.0)])
+  U, V = get_fe_space(trials_u,1), get_fe_space(tests_u,1)
+  Q = TestFESpace(model,reffe_p;conformity=:L2,constraint=:zeromean) 
+
+  mfs = BlockMultiFieldStyle()
+  X = MultiFieldFESpace([U,Q];style=mfs)
+  Y = MultiFieldFESpace([V,Q];style=mfs)
+
+  # Weak formulation
+  f = VectorValue(1.0,1.0)
+  biform_u(u,v,dΩ) = ∫(∇(v)⊙∇(u))dΩ
+  biform((u,p),(v,q),dΩ) = biform_u(u,v,dΩ) - ∫((∇⋅v)*p)dΩ - ∫((∇⋅u)*q)dΩ
+  liform((v,q),dΩ) = ∫(v⋅f)dΩ
+
+  # Assemble linear system
+  qdegree = 2*(fe_order+1) # Quadrature degree
+  Ω = Triangulation(model)
+  dΩ = Measure(Ω,qdegree)
+  op = AffineFEOperator((u,v)->biform(u,v,dΩ),v->liform(v,dΩ),X,Y)
+  A, b = get_matrix(op), get_vector(op)
+
+  # GMG preconditioner for the velocity block
+  biforms = map(mh) do mhl
+    get_bilinear_form(mhl,biform_u,qdegree)
+  end
+  smoothers = map(view(mh,1:num_levels(mh)-1)) do mhl
+    RichardsonSmoother(JacobiLinearSolver(),10,2.0/3.0)
+  end
+  restrictions, prolongations = setup_transfer_operators(
+    trials_u, qdegree; mode=:residual, solver=CGSolver(JacobiLinearSolver())
+  )
+  solver_u = GMGLinearSolver(
+    mh,trials_u,tests_u,biforms,
+    prolongations,restrictions,
+    pre_smoothers=smoothers,
+    post_smoothers=smoothers,
+    coarsest_solver=LUSolver(),
+    maxiter=4,mode=:solver
+  )
+
+  # PCG solver for the pressure block
+  solver_p = CGSolver(JacobiLinearSolver();maxiter=20,atol=1e-14,rtol=1.e-6)
+
+  # 2x2 Block triangular preconditioner
+  blocks = [LinearSystemBlock() LinearSystemBlock();
+            LinearSystemBlock() BiformBlock((p,q) -> ∫(p*q)dΩ,Q,Q)]
+  P = BlockTriangularSolver(blocks,[solver_u,solver_p])
+
+  # Global solver
+  solver = FGMRESSolver(10,P;rtol=1.e-8,verbose=i_am_main(parts))
+  ns = numerical_setup(symbolic_setup(solver,A),A)
+
+  # Solve
+  x = allocate_in_domain(A)
+  fill!(x,0.0)
+  solve!(x,ns,b)
+
+  # Postprocess
+  uh, ph = FEFunction(X,x)
+  writevtk(Ω,"demo",cellfields=["uh"=>uh,"ph"=>ph])
+end

joss_paper/docker.sh

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+sudo docker run -it --rm -v $(pwd):/data -u $(id -u):$(id -g) openjournals/inara -o pdf,crossref paper.md

joss_paper/packages.dot

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+# https://sketchviz.com/@JordiManyer/a34cdc3942aab5c0e011c05ce12bc2e5
+
+digraph G {
+  graph [fontname = "Handlee"];
+  node [fontname = "Handlee"];
+  edge [fontname = "Handlee",arrowhead=vee,arrowtail=vee];
+
+  bgcolor=transparent;
+
+  "Gridap.jl" -> "GridapDistributed.jl" [dir=back]
+  "Gridap.jl" -> "GridapPETSC.jl" [dir=back]
+  "PartitionedArrays.jl" -> "GridapPETSC.jl" [dir=back]
+  "PartitionedArrays.jl" -> "GridapDistributed.jl" [dir=back]
+  "GridapDistributed.jl" -> "GridapP4est.jl" [dir=back]
+  "GridapDistributed.jl" -> "GridapSolvers.jl" [dir=back]
+  "GridapPETSC.jl" -> "GridapSolvers.jl" [dir=back,style=dashed]
+  "GridapP4est.jl" -> "GridapSolvers.jl" [dir=back,style=dashed]
+
+  "Gridap.jl" [shape=rectangle]
+  "PartitionedArrays.jl" [shape=rectangle]
+  "GridapDistributed.jl" [shape=rectangle]
+  "GridapPETSC.jl" [shape=rectangle]
+  "GridapP4est.jl" [shape=rectangle]
+  "GridapSolvers.jl" [style=filled,shape=rectangle]
+}

joss_paper/packages.sh

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+#!/bin/bash
+
+dot -Tpng -opackages.png packages.dot