Updated MWEs

scripts/Embedded/Examples/CutFEM_2d_thermal_(island_checking).jl

@@ -0,0 +1,120 @@
+using Gridap,GridapTopOpt, GridapSolvers
+using Gridap.Adaptivity, Gridap.Geometry
+using GridapEmbedded, GridapEmbedded.LevelSetCutters
+
+using GridapTopOpt: StateParamIntegrandWithMeasure
+
+path="./results/CutFEM_thermal_compliance_ALM_island_detect/"
+rm(path,force=true,recursive=true)
+mkpath(path)
+n = 50
+order = 1
+γ = 0.1
+max_steps = floor(Int,order*n/5)
+vf = 0.4
+α_coeff = 4max_steps*γ
+iter_mod = 1
+
+_model = CartesianDiscreteModel((0,1,0,1),(n,n))
+base_model = UnstructuredDiscreteModel(_model)
+ref_model = refine(base_model, refinement_method = "barycentric")
+model = ref_model.model
+el_Δ = get_el_Δ(_model)
+h = maximum(el_Δ)
+h_refine = maximum(el_Δ)/2
+f_Γ_D(x) = (x[1] ≈ 0.0 && (x[2] <= 0.2 + eps() || x[2] >= 0.8 - eps()))
+f_Γ_N(x) = (x[1] ≈ 1 && 0.4 - eps() <= x[2] <= 0.6 + eps())
+update_labels!(1,model,f_Γ_D,"Gamma_D")
+update_labels!(2,model,f_Γ_N,"Gamma_N")
+
+## Triangulations and measures
+Ω = Triangulation(model)
+Γ_N = BoundaryTriangulation(model,tags="Gamma_N")
+dΩ = Measure(Ω,2*order)
+dΓ_N = Measure(Γ_N,2*order)
+vol_D = sum(∫(1)dΩ)
+
+## Levet-set function space and derivative regularisation space
+reffe_scalar = ReferenceFE(lagrangian,Float64,order)
+V_reg = TestFESpace(model,reffe_scalar;dirichlet_tags=["Gamma_N"])
+U_reg = TrialFESpace(V_reg,0)
+V_φ = TestFESpace(model,reffe_scalar)
+V_χ = TestFESpace(model,ReferenceFE(lagrangian,Float64,0))
+
+## Levet-set function
+φh = interpolate(x->-cos(4π*x[1])*cos(4π*x[2])-0.4,V_φ)
+Ωs = EmbeddedCollection(model,φh) do cutgeo,_
+  Ωin = DifferentiableTriangulation(Triangulation(cutgeo,PHYSICAL),V_φ)
+  Γ = DifferentiableTriangulation(EmbeddedBoundary(cutgeo),V_φ)
+  Γg = GhostSkeleton(cutgeo)
+  Ωact = Triangulation(cutgeo,ACTIVE)
+  (;
+    :Ωin  => Ωin,
+    :dΩin => Measure(Ωin,2*order),
+    :Γg   => Γg,
+    :dΓg  => Measure(Γg,2*order),
+    :n_Γg => get_normal_vector(Γg),
+    :Γ    => Γ,
+    :dΓ   => Measure(Γ,2*order),
+    :Ωact => Ωact,
+    :χ => GridapTopOpt.get_isolated_volumes_mask(cutgeo,["Gamma_D"])
+  )
+end
+
+## Weak form
+const γg = 0.1
+a(u,v,φ) = ∫(∇(v)⋅∇(u))Ωs.dΩin +
+  ∫((γg*h)*jump(Ωs.n_Γg⋅∇(v))*jump(Ωs.n_Γg⋅∇(u)))Ωs.dΓg +
+  ∫(Ωs.χ*v*u)Ωs.dΩin
+l(v,φ) = ∫(v)dΓ_N
+
+## Optimisation functionals
+J(u,φ) = a(u,u,φ)
+Vol(u,φ) = ∫(1/vol_D)Ωs.dΩin - ∫(vf/vol_D)dΩ
+dVol(q,u,φ) = ∫(-1/vol_D*q/(1e-20 + norm ∘ (∇(φ))))Ωs.dΓ
+
+## Setup solver and FE operators
+state_collection = EmbeddedCollection(model,φh) do _,_
+  V = TestFESpace(Ωs.Ωact,reffe_scalar;dirichlet_tags=["Gamma_D"])
+  U = TrialFESpace(V,0.0)
+  state_map = AffineFEStateMap(a,l,U,V,V_φ,U_reg,φh)
+  (;
+    :state_map => state_map,
+    :J => StateParamIntegrandWithMeasure(J,state_map),
+    :C => map(Ci -> StateParamIntegrandWithMeasure(Ci,state_map),[Vol,])
+  )
+end
+pcfs = EmbeddedPDEConstrainedFunctionals(state_collection;analytic_dC=(dVol,))
+
+## Evolution Method
+evo = CutFEMEvolve(V_φ,Ωs,dΩ,h;max_steps)
+reinit = StabilisedReinit(V_φ,Ωs,dΩ,h;stabilisation_method=ArtificialViscosity(3.0))#InteriorPenalty(V_φ))
+ls_evo = UnfittedFEEvolution(evo,reinit)
+reinit!(ls_evo,φh)
+
+## Hilbertian extension-regularisation problems
+α = α_coeff*(h_refine/order)^2
+a_hilb(p,q) =∫(α*∇(p)⋅∇(q) + p*q)dΩ;
+vel_ext = VelocityExtension(a_hilb,U_reg,V_reg)
+
+## Optimiser
+converged(m) = GridapTopOpt.default_al_converged(
+  m;
+  L_tol = 0.01*h_refine,
+  C_tol = 0.01
+)
+optimiser = AugmentedLagrangian(pcfs,ls_evo,vel_ext,φh;debug=true,
+  γ,verbose=true,constraint_names=[:Vol],converged)
+for (it,uh,φh,state) in optimiser
+  x_φ = get_free_dof_values(φh)
+  idx = findall(isapprox(0.0;atol=10^-10),x_φ)
+  !isempty(idx) && @warn "Boundary intersects nodes!"
+  if iszero(it % iter_mod)
+    writevtk(Ω,path*"Omega$it",cellfields=["φ"=>φh,"|∇(φ)|"=>(norm ∘ ∇(φh)),"uh"=>uh,"velh"=>FEFunction(V_φ,state.vel),"χ"=>Ωs.χ])
+    writevtk(Ωs.Ωin,path*"Omega_in$it",cellfields=["uh"=>uh])
+  end
+  write_history(path*"/history.txt",optimiser.history)
+end
+it = get_history(optimiser).niter; uh = get_state(pcfs)
+writevtk(Ω,path*"Omega$it",cellfields=["φ"=>φh,"|∇(φ)|"=>(norm ∘ ∇(φh)),"uh"=>uh,"χ"=>Ωs.χ])
+writevtk(Ωs.Ωin,path*"Omega_in$it",cellfields=["uh"=>uh])

scripts/Embedded/Examples/fsi/2-cutfem_navier-stokes_fsi.jl

@@ -60,7 +60,7 @@ dΓi = Measure(Γi,degree)
 
 # Setup FESpace
 
-uin(x) = VectorValue(x[2],0.0)
+uin(x) = VectorValue(x[2]*(1-x[2]),0.0)
 
 reffe_u = ReferenceFE(lagrangian,VectorValue{D,Float64},order,space=:P)
 reffe_p = ReferenceFE(lagrangian,Float64,order,space=:P)

scripts/Embedded/Examples/fsi/2-cutfem_stokes_fsi.jl

@@ -58,7 +58,7 @@ dΓi = Measure(Γi,degree)
 
 # Setup FESpace
 
-uin(x) = VectorValue(x[2],0.0)
+uin(x) = VectorValue(x[2]*(1-x[2]),0.0)
 
 reffe_u = ReferenceFE(lagrangian,VectorValue{D,Float64},order,space=:P)
 reffe_p = ReferenceFE(lagrangian,Float64,order,space=:P)

scripts/Embedded/Examples/fsi/5-Brinkmann_stokes_P1-P1_Ersatz_elast_fsi.jl

@@ -0,0 +1,132 @@
+using Gridap, Gridap.Geometry, Gridap.Adaptivity
+using GridapEmbedded, GridapEmbedded.LevelSetCutters
+using GridapTopOpt
+
+path = "./results/fsi testing/"
+mkpath(path)
+
+# Cut the background model
+n = 100
+partition = (n,n)
+D = length(partition)
+_model = CartesianDiscreteModel((0,1,0,1),partition)
+base_model = UnstructuredDiscreteModel(_model)
+ref_model = refine(base_model, refinement_method = "barycentric")
+model = ref_model.model
+
+el_Δ = get_el_Δ(_model)
+h = maximum(el_Δ)
+f_Γ_D(x) = x[1] ≈ 0
+f_Γ_NoSlipTop(x) = x[2] ≈ 1
+f_Γ_NoSlipBottom(x) = x[2] ≈ 0
+update_labels!(1,model,f_Γ_D,"Gamma_D")
+update_labels!(2,model,f_Γ_NoSlipTop,"Gamma_NoSlipTop")
+update_labels!(3,model,f_Γ_NoSlipBottom,"Gamma_NoSlipBottom")
+
+# Cut the background model
+reffe_scalar = ReferenceFE(lagrangian,Float64,1)
+V_φ = TestFESpace(model,reffe_scalar)
+φh = interpolate(x->-max(20*abs(x[1]-0.5),3*abs(x[2]-0.2))+1,V_φ)
+geo = DiscreteGeometry(φh,model)
+cutgeo = cut(model,geo)
+cutgeo_facets = cut_facets(model,geo)
+
+# Generate the "active" model
+Ω_act = Triangulation(model)
+
+# Setup integration meshes
+Ω = Triangulation(cutgeo,PHYSICAL)
+Ωout = Triangulation(cutgeo,PHYSICAL_OUT)
+Γ = EmbeddedBoundary(cutgeo)
+Γg = GhostSkeleton(cutgeo)
+Γi = SkeletonTriangulation(cutgeo_facets)
+
+# Setup normal vectors
+n_Γ = get_normal_vector(Γ)
+n_Γg = get_normal_vector(Γg)
+n_Γi = get_normal_vector(Γi)
+
+# Setup Lebesgue measures
+order = 1
+degree = 2*order
+dΩ = Measure(Ω,degree)
+dΩout = Measure(Ωout,degree)
+dΓ = Measure(Γ,degree)
+dΓg = Measure(Γg,degree)
+dΓi = Measure(Γi,degree)
+
+# Setup FESpace
+
+uin(x) = VectorValue(x[2]*(1-x[2]),0.0) # Change this!!
+
+reffe_u = ReferenceFE(lagrangian,VectorValue{D,Float64},order,space=:P)
+reffe_p = ReferenceFE(lagrangian,Float64,order,space=:P)
+reffe_d = ReferenceFE(lagrangian,VectorValue{D,Float64},order)
+
+V = TestFESpace(Ω_act,reffe_u,conformity=:H1,dirichlet_tags=["Gamma_D","Gamma_NoSlipTop","Gamma_NoSlipBottom"])
+Q = TestFESpace(Ω_act,reffe_p,conformity=:H1)
+T = TestFESpace(Ω_act ,reffe_d,conformity=:H1,dirichlet_tags=["Gamma_NoSlipBottom"])
+
+U = TrialFESpace(V,[uin,VectorValue(0.0,0.0),VectorValue(0.0,0.0)])
+P = TrialFESpace(Q)
+R = TrialFESpace(T)
+
+X = MultiFieldFESpace([U,P,R])
+Y = MultiFieldFESpace([V,Q,T])
+
+# Weak form
+## Fluid
+# Properties
+Re = 60 # Reynolds number
+ρ = 1.0 # Density
+L = 1.0 # Characteristic length
+u0_max = maximum(abs,get_dirichlet_dof_values(U))
+μ = ρ*L*u0_max/Re # Viscosity
+# Stabilization parameters
+β1 = 0.2
+γ = 1000.0
+
+# Terms
+σf_n(u,p) = μ*∇(u)⋅n_Γ - p*n_Γ
+a_Ω(u,v) = μ*(∇(u) ⊙ ∇(v))
+b_Ω(v,p) = - (∇⋅v)*p
+c_Ω(p,q) = (β1*h^2)*∇(p)⋅∇(q)
+
+a_fluid((u,p),(v,q)) =
+  ∫( a_Ω(u,v)+b_Ω(u,q)+b_Ω(v,p)-c_Ω(p,q) ) * dΩ +
+  ∫( a_Ω(u,v)+b_Ω(u,q)+b_Ω(v,p)-c_Ω(p,q) + (γ/h)*u⋅v ) * dΩout
+
+## Structure
+# Stabilization and material parameters
+function lame_parameters(E,ν)
+  λ = (E*ν)/((1+ν)*(1-2*ν))
+  μ = E/(2*(1+ν))
+  (λ, μ)
+end
+λs, μs = lame_parameters(1.0,0.3)
+ϵ = (λs + 2μs)*1e-3
+# Terms
+σ(ε) = λs*tr(ε)*one(ε) + 2*μs*ε
+a_solid(d,s) = ∫(ε(s) ⊙ (σ ∘ ε(d)))dΩout +
+  ∫(ϵ*(ε(s) ⊙ (σ ∘ ε(d))))dΩ # Ersatz
+
+## Full problem
+a((u,p,d),(v,q,s)) = a_fluid((u,p),(v,q)) + a_solid(d,s) +
+  ∫(σf_n(u,p) ⋅ s)dΓ # plus sign because of the normal direction
+l((v,q,s)) = 0.0
+
+op = AffineFEOperator(a,l,X,Y)
+
+uh, ph, dh = solve(op)
+
+# Mass flow rate through surface (this should be close to zero)
+@show m = sum(∫(ρ*uh⋅n_Γ)dΓ)
+
+writevtk(Ω_act,path*"fsi-stokes-brinkmann_elast-ersatz_full",
+  cellfields=["uh"=>uh,"ph"=>ph,"dh"=>dh])
+writevtk(Ω,path*"fsi-stokes-brinkmann_elast-ersatz_fluid",
+  cellfields=["uh"=>uh,"ph"=>ph,"dh"=>dh])
+writevtk(Ωout,path*"fsi-stokes-brinkmann_elast-ersatz_solid",
+  cellfields=["uh"=>uh,"ph"=>ph,"dh"=>dh])
+
+writevtk(Γ,path*"fsi-stokes-brinkmann_elast-ersatz_interface",cellfields=["σ⋅n"=>(σ ∘ ε(dh))⋅n_Γ,"σf_n"=>σf_n(uh,ph)])

scripts/Embedded/MWEs/isolated_volumes.jl

@@ -6,31 +6,33 @@ using GridapEmbedded.LevelSetCutters
 using Gridap.Geometry, Gridap.FESpaces, Gridap.CellData, Gridap.Adaptivity, Gridap.Arrays
 
 order = 1
-n = 100
+n = 41
 model = UnstructuredDiscreteModel(CartesianDiscreteModel((0,1,0,1),(n,n)))
+update_labels!(1,model,x->x[1]≈0,"Gamma_D")
 Ω = Triangulation(model)
 
 reffe_scalar = ReferenceFE(lagrangian,Float64,order)
 V_φ = TestFESpace(model,reffe_scalar)
 
-φh = interpolate(x->cos(2π*x[1])*cos(2π*x[2])-0.11,V_φ)
-
-# R = 0.195
-# R = 0.2 # This fails
-# f(x0,r) = x -> sqrt((x[1]-x0[1])^2 + (x[2]-x0[2])^2) - r
-# φh = interpolate(x->-f([0.5,0.5],R)(x),V_φ)
-# φh = interpolate(x->min(f([0.25,0.5],R)(x),f([0.75,0.5],R)(x)),V_φ)
+f(x,y0) = abs(x[2]-y0) - 0.05
+g(x,x0,y0,r) = sqrt((x[1]-x0)^2 + (x[2]-y0)^2) - r
+f(x) = min(f(x,0.75),f(x,0.25),
+  g(x,0.15,0.5,0.1),
+  g(x,0.5,0.6,0.2),
+  g(x,0.85,0.5,0.1),
+  g(x,0.5,0.15,0.05))
+φh = interpolate(f,V_φ)
 
 geo = DiscreteGeometry(φh,model)
 cutgeo = cut(model,geo)
 
 bgcell_to_inoutcut = compute_bgcell_to_inoutcut(model,geo)
 cell_to_color, color_to_group = GridapTopOpt.tag_isolated_volumes(model,bgcell_to_inoutcut;groups=((GridapTopOpt.CUT,IN),OUT))
 
-color_to_tagged = GridapTopOpt.find_tagged_volumes(model,["tag_5","tag_7"],cell_to_color,color_to_group)
+color_to_tagged = GridapTopOpt.find_tagged_volumes(model,["Gamma_D"],cell_to_color,color_to_group)
 cell_to_tagged = map(c -> color_to_tagged[c], cell_to_color)
 
-μ = GridapTopOpt.get_isolated_volumes_mask(cutgeo,["tag_5","tag_7"])
+μ = GridapTopOpt.get_isolated_volumes_mask(cutgeo,["Gamma_D"])
 
 writevtk(
   Ω,"results/background",

test/seq/IsolatedVolumeTests.jl

@@ -0,0 +1 @@
+# TODO