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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,91 @@ | ||
| using LevelSetTopOpt, Gridap, GridapDistributed, GridapPETSc, PartitionedArrays, | ||
| SparseMatricesCSR | ||
|
|
||
| function main(mesh_partition,distribute,use_l::Bool) | ||
| ranks = distribute(LinearIndices((prod(mesh_partition),))) | ||
| # FE parameters | ||
| order = 1 # Finite element order | ||
| xmax = ymax = 1.0 # Domain size | ||
| dom = (0,xmax,0,ymax) # Bounding domain | ||
| el_size = (200,200) # Mesh partition size | ||
| prop_Γ_N = 0.2 # Γ_N size parameter | ||
| prop_Γ_D = 0.2 # Γ_D size parameter | ||
| f_Γ_N(x) = (x[1] ≈ xmax && # Γ_N indicator function | ||
| ymax/2-ymax*prop_Γ_N/2 - eps() <= x[2] <= ymax/2+ymax*prop_Γ_N/2 + eps()) | ||
| f_Γ_D(x) = (x[1] ≈ 0.0 && # Γ_D indicator function | ||
| (x[2] <= ymax*prop_Γ_D + eps() || x[2] >= ymax-ymax*prop_Γ_D - eps())) # @$\lvert\lvert$@ | ||
| # FD parameters | ||
| γ = 0.1 # HJ eqn time step coeff | ||
| γ_reinit = 0.5 # Reinit. eqn time step coeff | ||
| max_steps = floor(Int,minimum(el_size)/10) # Max steps for advection | ||
| tol = 1/(5order^2)/minimum(el_size) # Advection tolerance | ||
| # Problem parameters | ||
| κ = 1 # Diffusivity | ||
| g = 1 # Heat flow in | ||
| vf = 0.4 # Volume fraction constraint | ||
| lsf_func = initial_lsf(4,0.2) # Initial level set function | ||
| iter_mod = 10 # VTK Output modulo | ||
| path = "./results/AD_tut1_MPI_lobj_$use_l/" # Output path | ||
| i_am_main(ranks) && mkpath(path) # Create path | ||
| # Model | ||
| model = CartesianDiscreteModel(ranks,mesh_partition,dom,el_size); | ||
| update_labels!(1,model,f_Γ_D,"Gamma_D") | ||
| update_labels!(2,model,f_Γ_N,"Gamma_N") | ||
| # Triangulation and measures | ||
| Ω = Triangulation(model) | ||
| Γ_N = BoundaryTriangulation(model,tags="Gamma_N") | ||
| dΩ = Measure(Ω,2*order) | ||
| dΓ_N = Measure(Γ_N,2*order) | ||
| # Spaces | ||
| reffe = ReferenceFE(lagrangian,Float64,order) | ||
| V = TestFESpace(model,reffe;dirichlet_tags=["Gamma_D"]) | ||
| U = TrialFESpace(V,0.0) | ||
| V_φ = TestFESpace(model,reffe) | ||
| V_reg = TestFESpace(model,reffe;dirichlet_tags=["Gamma_N"]) | ||
| U_reg = TrialFESpace(V_reg,0) | ||
| # Level set and interpolator | ||
| φh = interpolate(lsf_func,V_φ) | ||
| interp = SmoothErsatzMaterialInterpolation(η = 2*maximum(get_el_Δ(model))) | ||
| I,H,DH,ρ = interp.I,interp.H,interp.DH,interp.ρ | ||
| # Weak formulation | ||
| a(u,v,φ,dΩ,dΓ_N) = ∫((I ∘ φ)*κ*∇(u)⋅∇(v))dΩ | ||
| l(v,φ,dΩ,dΓ_N) = ∫(g*v)dΓ_N | ||
| state_map = AffineFEStateMap(a,l,U,V,V_φ,U_reg,φh,dΩ,dΓ_N) | ||
| # Objective and constraints | ||
| J(u,φ,dΩ,dΓ_N) = if use_l | ||
| ∫(g*u)dΓ_N #+ ∫(0)dΩ | ||
| else | ||
| ∫((I ∘ φ)*κ*∇(u)⋅∇(u))dΩ | ||
| end | ||
| dJ(q,u,φ,dΩ,dΓ_N) = ∫(κ*∇(u)⋅∇(u)*q*(DH ∘ φ)*(norm ∘ ∇(φ)))dΩ | ||
| vol_D = sum(∫(1)dΩ) | ||
| C(u,φ,dΩ,dΓ_N) = ∫(((ρ ∘ φ) - vf)/vol_D)dΩ | ||
| dC(q,u,φ,dΩ,dΓ_N) = ∫(-1/vol_D*q*(DH ∘ φ)*(norm ∘ ∇(φ)))dΩ | ||
| pcfs = PDEConstrainedFunctionals(J,[C],state_map) | ||
| # Velocity extension | ||
| α = 4*maximum(get_el_Δ(model)) | ||
| a_hilb(p,q) =∫(α^2*∇(p)⋅∇(q) + p*q)dΩ | ||
| vel_ext = VelocityExtension(a_hilb, U_reg, V_reg) | ||
| # Finite difference scheme | ||
| scheme = FirstOrderStencil(length(el_size),Float64) | ||
| stencil = AdvectionStencil(scheme,model,V_φ,tol,max_steps) | ||
| # Optimiser | ||
| optimiser = AugmentedLagrangian(pcfs,stencil,vel_ext,φh; | ||
| γ,γ_reinit,verbose=i_am_main(ranks),constraint_names=[:Vol]) | ||
| # Solve | ||
| for (it,uh,φh) in optimiser | ||
| data = ["φ"=>φh,"H(φ)"=>(H ∘ φh),"|nabla(φ)|"=>(norm ∘ ∇(φh)),"uh"=>uh] | ||
| iszero(it % iter_mod) && (writevtk(Ω,path*"out$it",cellfields=data);GC.gc()) | ||
| write_history(path*"/history.txt",get_history(optimiser);ranks) | ||
| end | ||
| # Final structure | ||
| it = get_history(optimiser).niter; uh = get_state(pcfs) | ||
| writevtk(Ω,path*"out$it",cellfields=["φ"=>φh, | ||
| "H(φ)"=>(H ∘ φh),"|nabla(φ)|"=>(norm ∘ ∇(φh)),"uh"=>uh]) | ||
| end | ||
|
|
||
| with_mpi() do distribute | ||
| mesh_partition = (2,2) | ||
| main(mesh_partition,distribute,false) | ||
| main(mesh_partition,distribute,true) # <- this should crash | ||
| end |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,87 @@ | ||
| using LevelSetTopOpt, Gridap | ||
|
|
||
| function main(use_l::Bool) | ||
| # FE parameters | ||
| order = 1 # Finite element order | ||
| xmax = ymax = 1.0 # Domain size | ||
| dom = (0,xmax,0,ymax) # Bounding domain | ||
| el_size = (200,200) # Mesh partition size | ||
| prop_Γ_N = 0.2 # Γ_N size parameter | ||
| prop_Γ_D = 0.2 # Γ_D size parameter | ||
| f_Γ_N(x) = (x[1] ≈ xmax && # Γ_N indicator function | ||
| ymax/2-ymax*prop_Γ_N/2 - eps() <= x[2] <= ymax/2+ymax*prop_Γ_N/2 + eps()) | ||
| f_Γ_D(x) = (x[1] ≈ 0.0 && # Γ_D indicator function | ||
| (x[2] <= ymax*prop_Γ_D + eps() || x[2] >= ymax-ymax*prop_Γ_D - eps())) | ||
| # FD parameters | ||
| γ = 0.1 # HJ eqn time step coeff | ||
| γ_reinit = 0.5 # Reinit. eqn time step coeff | ||
| max_steps = floor(Int,minimum(el_size)/10) # Max steps for advection | ||
| tol = 1/(5order^2)/minimum(el_size) # Reinitialisation tolerance | ||
| # Problem parameters | ||
| κ = 1 # Diffusivity | ||
| g = 1 # Heat flow in | ||
| vf = 0.4 # Volume fraction constraint | ||
| lsf_func = initial_lsf(4,0.2) # Initial level set function | ||
| iter_mod = 10 # VTK Output modulo | ||
| path = "./results/tut1_lobj_$use_l/" # Output path | ||
| mkpath(path) # Create path | ||
| # Model | ||
| model = CartesianDiscreteModel(dom,el_size); | ||
| update_labels!(1,model,f_Γ_D,"Gamma_D") | ||
| update_labels!(2,model,f_Γ_N,"Gamma_N") | ||
| # Triangulation and measures | ||
| Ω = Triangulation(model) | ||
| Γ_N = BoundaryTriangulation(model,tags="Gamma_N") | ||
| dΩ = Measure(Ω,2*order) | ||
| dΓ_N = Measure(Γ_N,2*order) | ||
| # Spaces | ||
| reffe = ReferenceFE(lagrangian,Float64,order) | ||
| V = TestFESpace(model,reffe;dirichlet_tags=["Gamma_D"]) | ||
| U = TrialFESpace(V,0.0) | ||
| V_φ = TestFESpace(model,reffe) | ||
| V_reg = TestFESpace(model,reffe;dirichlet_tags=["Gamma_N"]) | ||
| U_reg = TrialFESpace(V_reg,0) | ||
| # Level set and interpolator | ||
| φh = interpolate(lsf_func,V_φ) | ||
| interp = SmoothErsatzMaterialInterpolation(η = 2*maximum(get_el_Δ(model))) | ||
| I,H,DH,ρ = interp.I,interp.H,interp.DH,interp.ρ | ||
| # Weak formulation | ||
| a(u,v,φ,dΩ,dΓ_N) = ∫((I ∘ φ)*κ*∇(u)⋅∇(v))dΩ | ||
| l(v,φ,dΩ,dΓ_N) = ∫(g*v)dΓ_N | ||
| state_map = AffineFEStateMap(a,l,U,V,V_φ,U_reg,φh,dΩ,dΓ_N) | ||
| # Objective and constraints | ||
| J(u,φ,dΩ,dΓ_N) = if use_l | ||
| ∫(g*u)dΓ_N | ||
| else | ||
| ∫((I ∘ φ)*κ*∇(u)⋅∇(u))dΩ | ||
| end | ||
| dJ(q,u,φ,dΩ,dΓ_N) = ∫(κ*∇(u)⋅∇(u)*q*(DH ∘ φ)*(norm ∘ ∇(φ)))dΩ | ||
| vol_D = sum(∫(1)dΩ) | ||
| C(u,φ,dΩ,dΓ_N) = ∫(((ρ ∘ φ) - vf)/vol_D)dΩ | ||
| dC(q,u,φ,dΩ,dΓ_N) = ∫(-1/vol_D*q*(DH ∘ φ)*(norm ∘ ∇(φ)))dΩ | ||
| pcfs = PDEConstrainedFunctionals(J,[C],state_map, | ||
| analytic_dJ=dJ,analytic_dC=[dC]) | ||
| # Velocity extension | ||
| α = 4*maximum(get_el_Δ(model)) | ||
| a_hilb(p,q) =∫(α^2*∇(p)⋅∇(q) + p*q)dΩ | ||
| vel_ext = VelocityExtension(a_hilb,U_reg,V_reg) | ||
| # Finite difference scheme | ||
| scheme = FirstOrderStencil(length(el_size),Float64) | ||
| stencil = AdvectionStencil(scheme,model,V_φ,tol,max_steps) | ||
| # Optimiser | ||
| optimiser = AugmentedLagrangian(pcfs,stencil,vel_ext,φh; | ||
| γ,γ_reinit,verbose=true,constraint_names=[:Vol]) | ||
| # Solve | ||
| for (it,uh,φh) in optimiser | ||
| data = ["φ"=>φh,"H(φ)"=>(H ∘ φh),"|∇(φ)|"=>(norm ∘ ∇(φh)),"uh"=>uh] | ||
| iszero(it % iter_mod) && (writevtk(Ω,path*"out$it",cellfields=data);GC.gc()) | ||
| write_history(path*"/history.txt",get_history(optimiser)) | ||
| end | ||
| # Final structure | ||
| it = get_history(optimiser).niter; uh = get_state(pcfs) | ||
| writevtk(Ω,path*"out$it",cellfields=["φ"=>φh, | ||
| "H(φ)"=>(H ∘ φh),"|∇(φ)|"=>(norm ∘ ∇(φh)),"uh"=>uh]) | ||
| end | ||
|
|
||
| main(false) | ||
| main(true) |