add unfitted evolution struct

scripts/Embedded/MWEs/Unfitted_Evolve&Reinit/unfitted_evolution.jl

@@ -0,0 +1,119 @@
+struct UnfittedFEEvolution <: GridapTopOpt.LevelSetEvolution
+  spaces
+  params
+  ode_solver
+  reinit_nls
+  function UnfittedFEEvolution(Ut_φ, V_φ, dΩ, h;
+      ode_ls = LUSolver(),
+      ode_nl = NLSolver(ode_ls, show_trace=true, method=:newton, iterations=10),
+      ode_solver = RungeKutta(ode_nl, ode_ls, 0.01, :DIRK_CrankNicolson_2_2),
+      NT = 10,
+      c = 0.1,
+      reinit_nls = NLSolver(ftol=1e-14, iterations = 50, show_trace=true)
+    )
+    spaces = (Ut_φ,V_φ)
+    params = (;NT,h,c,dΩ)
+    return new(spaces,params,ode_solver,reinit_nls)
+  end
+end
+
+function GridapTopOpt.evolve!(s::UnfittedFEEvolution,φ::AbstractArray,args...)
+  _, V_φ = s.spaces
+  evolve!(s,FEFunction(V_φ,φ),args...)
+end
+
+# Based on:
+# @article{
+#   Burman_Elfverson_Hansbo_Larson_Larsson_2018,
+#   title={Shape optimization using the cut finite element method},
+#   volume={328},
+#   ISSN={00457825},
+#   DOI={10.1016/j.cma.2017.09.005},
+#   journal={Computer Methods in Applied Mechanics and Engineering},
+#   author={Burman, Erik and Elfverson, Daniel and Hansbo, Peter and Larson, Mats G. and Larsson, Karl},
+#   year={2018},
+#   month=jan,
+#   pages={242–261},
+#   language={en}
+# }
+function GridapTopOpt.evolve!(s::UnfittedFEEvolution,φh,vel,γ)
+  Ut_φ, V_φ = s.spaces
+  params = s.params
+  NT, h, c, dΩ = params.NT, params.h, params.c, params.dΩ
+  # ode_solver = s.ode_solver
+  Tf = γ*NT
+  velh = FEFunction(V_φ,vel)
+
+  # This is temp as can't update γ in ode_solver yet
+  ode_ls = LUSolver()
+  ode_nl = NLSolver(ode_ls, show_trace=true, method=:newton, iterations=10)
+  ode_solver = RungeKutta(ode_nl, ode_ls, γ, :DIRK_CrankNicolson_2_2)
+
+  ϵ = 1e-20
+
+  geo = DiscreteGeometry(φh,model)
+  F = EmbeddedFacetDiscretization(LevelSetCutter(),model,geo)
+  FΓ = SkeletonTriangulation(F)
+  dFΓ = Measure(FΓ,2*order)
+  n = get_normal_vector(FΓ)
+
+  d1(∇u) = 1/(ϵ + norm(∇u))
+  _n(∇u) = ∇u/(ϵ + norm(∇u))
+  β = velh*∇(φh)/(ϵ + norm ∘ ∇(φh))
+  stiffness(t,u,v) = ∫((β ⋅ ∇(u)) * v)dΩ + ∫(c*h^2*jump(∇(u) ⋅ n)*jump(∇(v) ⋅ n))dFΓ
+  mass(t, ∂ₜu, v) = ∫(∂ₜu * v)dΩ
+  forcing(t,v) = ∫(0v)dΩ
+
+  op = TransientLinearFEOperator((stiffness,mass),forcing,Ut_φ,V_φ,constant_forms=(true,true))
+  uht = solve(ode_solver,op,0.0,Tf,φh)
+  for (t,uh) in uht
+    if t ≈ Tf
+      copyto!(get_free_dof_values(φh),get_free_dof_values(uh))
+    end
+  end
+end
+
+function GridapTopOpt.reinit!(s::UnfittedFEEvolution,φ::AbstractArray,args...)
+  _, V_φ = s.spaces
+  reinit!(s,FEFunction(V_φ,φ),args...)
+end
+
+# Based on:
+# @article{
+#   Mallon_Thornton_Hill_Badia,
+#   title={NEURAL LEVEL SET TOPOLOGY OPTIMIZATION USING UNFITTED FINITE ELEMENTS},
+#   author={Mallon, Connor N and Thornton, Aaron W and Hill, Matthew R and Badia, Santiago},
+#   language={en}
+# }
+function GridapTopOpt.reinit!(s::UnfittedFEEvolution,φh,args...)
+  Ut_φ, V_φ = s.spaces
+  params = s.params
+  NT, h, c, dΩ = params.NT, params.h, params.c, params.dΩ
+  reinit_nls = s.reinit_nls
+
+  γd = 20
+  cₐ = 0.5 # <- 3 in connor's paper
+  ϵ = 1e-20
+
+  # Tmp
+  geo = DiscreteGeometry(φh,model)
+  cutgeo = cut(model,geo)
+  Γ = EmbeddedBoundary(cutgeo)
+  dΓ = Measure(Γ,2*order)
+
+  sgn(ϕ₀) = sign ∘ ϕ₀
+  d1(∇u) = 1 / ( ϵ + norm(∇u) )
+  W(u) =  sgn(u) * ∇(u) * (d1 ∘ (∇(u)))
+  νₐ(w) = cₐ*h*(sqrt∘( w ⋅ w ))
+  a_ν(w,u,v) = ∫((γd/h)*v*u)dΓ + ∫(νₐ(W(w))*∇(u)⋅∇(v) + v*W(w)⋅∇(u))dΩ
+  b_ν(w,v) = ∫( sgn(w)*v )dΩ
+  res(u,v)    = a_ν(u,u,v)  - b_ν(u,v)
+  jac(u,du,v)  = a_ν(u,du,v)
+
+  op = FEOperator(res,jac,V_φ,V_φ)
+  Gridap.solve!(φh,reinit_nls,op)
+end
+
+function GridapTopOpt.get_dof_Δ(s::UnfittedFEEvolution)
+  s.params.h
+end

scripts/Embedded/MWEs/Unfitted_Evolve&Reinit/unitted_evolution_test.jl

@@ -0,0 +1,39 @@
+using GridapTopOpt
+
+using Gridap
+
+using GridapEmbedded
+using GridapEmbedded.LevelSetCutters
+using Gridap.Geometry, Gridap.FESpaces, Gridap.CellData, Gridap.ODEs
+import Gridap.Geometry: get_node_coordinates, collect1d
+
+include("unfitted_evolution.jl")
+include("../../differentiable_trians.jl")
+
+order = 1
+n = 101
+
+_model = CartesianDiscreteModel((0,1,0,1),(n,n))
+cd = Gridap.Geometry.get_cartesian_descriptor(_model)
+h = maximum(cd.sizes)
+
+model = simplexify(_model)
+Ω = Triangulation(model)
+dΩ = Measure(Ω,2*order)
+reffe_scalar = ReferenceFE(lagrangian,Float64,order)
+V_φ = TestFESpace(model,reffe_scalar)
+Ut_φ = TransientTrialFESpace(V_φ,t -> (x->-1))
+
+φh = interpolate(x->cos(2π*x[1])*cos(2π*x[2])-0.11,V_φ)
+
+ls_evo = UnfittedFEEvolution(Ut_φ, V_φ, dΩ, h; NT = 5, c = 0.1)
+
+reinit!(ls_evo,φh)
+velh = interpolate(x->-1,V_φ)
+evolve!(ls_evo,φh,get_free_dof_values(velh),0.01)
+reinit!(ls_evo,φh)
+
+writevtk(
+  Ω,"results/test_evolve",
+  cellfields=["φh"=>φh,"|∇φh|"=>norm ∘ ∇(φh)]
+)