diff --git a/scripts/Embedded/Examples/fsi/gmsh/GMSH_TO-6-Brinkmann_stokes_P2-P1_Ersatz_elast_fsi.jl b/scripts/Embedded/Examples/fsi/gmsh/GMSH_TO-6-Brinkmann_stokes_P2-P1_Ersatz_elast_fsi.jl index fb2dd3e..d8fe2ab 100644 --- a/scripts/Embedded/Examples/fsi/gmsh/GMSH_TO-6-Brinkmann_stokes_P2-P1_Ersatz_elast_fsi.jl +++ b/scripts/Embedded/Examples/fsi/gmsh/GMSH_TO-6-Brinkmann_stokes_P2-P1_Ersatz_elast_fsi.jl @@ -5,11 +5,11 @@ using GridapTopOpt ############# -path = "./results/GMSH-TO-6-Brinkmann_stokes_P2-P1_Ersatz_elast_fsi/results/" +path = "./results/GMSH-TO-6-Brinkmann_stokes_P2-P1_Ersatz_elast_fsi_multistage_reinit/results/" mkpath(path) -γ_evo = 0.2 -max_steps = 20 +γ_evo = 3.0 +max_steps = 1 vf = 0.025 α_coeff = 2 iter_mod = 1 @@ -109,7 +109,7 @@ u0_max = maximum(abs,get_dirichlet_dof_values(U)) μ = ρ*cl*u0_max/Re # Viscosity ν = μ/ρ # Kinematic viscosity # Stabilization parameters -γ(h) = 1e5*μ/h +γ(h) = 1000/h #1e5*μ/h # Terms σf_n(u,p,n) = μ*∇(u) ⋅ n - p*n @@ -118,7 +118,7 @@ b_Ω(v,p) = - (∇⋅v)*p a_fluid((u,p),(v,q)) = ∫( a_Ω(u,v)+b_Ω(u,q)+b_Ω(v,p)) * Ω.dΩf + - ∫( a_Ω(u,v)+b_Ω(u,q)+b_Ω(v,p) + (γ∘hₕ)*u⋅v ) * Ω.dΩs + ∫( a_Ω(u,v)+b_Ω(u,q)+b_Ω(v,p) + (γ(hmin))*u⋅v ) * Ω.dΩs ## Structure # Stabilization and material parameters @@ -154,13 +154,18 @@ state_map = AffineFEStateMap(a_coupled,l_coupled,X,Y,V_φ,U_reg,φh) pcfs = PDEConstrainedFunctionals(J_comp,[Vol],state_map) ## Evolution Method -evo = CutFEMEvolve(V_φ,Ω,dΩ_act,hₕ;max_steps) -reinit = StabilisedReinit(V_φ,Ω,dΩ_act,hₕ;stabilisation_method=ArtificialViscosity(3.0)) +# evo = CutFEMEvolve(V_φ,Ω,dΩ_act,hmin;max_steps,γg=0.075) +# reinit = StabilisedReinit(V_φ,Ω,dΩ_act,hmin;stabilisation_method=ArtificialViscosity(3.0)) +# ls_evo = UnfittedFEEvolution(evo,reinit) +evo = CutFEMEvolve(V_φ,Ω,dΩ_act,hₕ;max_steps,γg=0.1) +reinit1 = StabilisedReinit(V_φ,Ω,dΩ_act,hₕ;stabilisation_method=ArtificialViscosity(2.0)) +reinit2 = StabilisedReinit(V_φ,Ω,dΩ_act,hₕ;stabilisation_method=GridapTopOpt.InteriorPenalty2(V_φ,γg=1.0)) +reinit = GridapTopOpt.MultiStageStabilisedReinit2([reinit1,reinit2]) ls_evo = UnfittedFEEvolution(evo,reinit) ## Hilbertian extension-regularisation problems _α(hₕ) = (α_coeff*hₕ)^2 -a_hilb(p,q) =∫((_α ∘ hₕ)*∇(p)⋅∇(q) + p*q)dΩ_act; +a_hilb(p,q) =∫((_α(hmin))*∇(p)⋅∇(q) + p*q)dΩ_act; vel_ext = VelocityExtension(a_hilb,U_reg,V_reg) ## Optimiser diff --git a/scripts/Embedded/Examples/fsi/gmsh/mesh_finer.msh b/scripts/Embedded/Examples/fsi/gmsh/mesh_finer.msh new file mode 100644 index 0000000..c2ec598 --- /dev/null +++ b/scripts/Embedded/Examples/fsi/gmsh/mesh_finer.msh @@ -0,0 +1,108738 @@ +$MeshFormat +4.1 0 8 +$EndMeshFormat +$PhysicalNames +12 +0 23 "Gamma_f_D" +0 25 "Gamma_f_N" +0 27 "Gamma_NoSlipTop" +0 30 "Gamma_s_D" +0 33 "Omega_NonDesign" +1 22 "Gamma_f_D" +1 24 "Gamma_f_N" +1 26 "Gamma_NoSlipTop" +1 28 "Gamma_NoSlipBottom" +1 29 "Gamma_s_D" +1 32 "Omega_NonDesign" +2 31 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26897 25822 +54694 25663 26907 26813 +54695 25113 26905 26758 +54696 26811 26923 25159 +54697 25870 26935 26801 +54698 26785 26929 25729 +54699 25174 26913 26787 +54700 26831 26930 26314 +54701 25547 26936 26751 +54702 26782 26928 25109 +$EndElements diff --git a/src/LevelSetEvolution/UnfittedEvolution/CutFEMEvolve.jl b/src/LevelSetEvolution/UnfittedEvolution/CutFEMEvolve.jl index 2b637c5..5de013a 100644 --- a/src/LevelSetEvolution/UnfittedEvolution/CutFEMEvolve.jl +++ b/src/LevelSetEvolution/UnfittedEvolution/CutFEMEvolve.jl @@ -55,7 +55,25 @@ function get_transient_operator(φh,velh,s::CutFEMEvolve) γg, h, dΓg, n_Γg = params.γg, params.h, params.dΓg, params.n_Γg ϵ = 1e-20 + # V_reg2 = TestFESpace(get_triangulation(V_φ).model, + # ReferenceFE(lagrangian,VectorValue{2,Float64},1);dirichlet_tags=["Omega_NonDesign","Gamma_s_D"]) + # U_reg2 = TrialFESpace(V_reg2) + + # _α(hₕ) = 3(hₕ)^2 + # a_hilb2(p,q) =∫((_α(h))*∇(p) ⊙ ∇(q) + p ⋅ q)dΩ_bg; + # vel_ext2 = VelocityExtension(a_hilb2,U_reg2,V_reg2) + # _n(∇φh) = ∇φh/(1e-20 + norm(∇φh)) + # # l_n(v) = ∫((velh*(_n ∘ ∇(φh)) ⋅ v))dΩ_bg + # l_n(v) = ∫((velh*(s.Ωs.n_Γ ⋅ v)))s.Ωs.dΓ + # _b = assemble_vector(l_n,V_reg2) + # project!(vel_ext2,_b) + # n_regh = FEFunction(V_reg2,_b) + # β = n_regh/sqrt(dot(_b,vel_ext2.K*_b)) + + # writevtk(get_triangulation(φh),"results/beta",cellfields=["beta"=>β]) v_norm = maximum(abs,get_free_dof_values(velh)) + # β(vh,n) = vh/(ϵ + v_norm) * n/(ϵ + norm(n)) + # β(vh,n) = n/(ϵ + norm(n)) β(vh,∇φ) = vh/(ϵ + v_norm) * ∇φ/(ϵ + norm(∇φ)) γ(h) = γg*h^2 @@ -63,7 +81,17 @@ function get_transient_operator(φh,velh,s::CutFEMEvolve) aₛ(u,v,h::CellField) = ∫(mean(γ ∘ h)*jump(∇(u) ⋅ n_Γg)*jump(∇(v) ⋅ n_Γg))dΓg aₛ(u,v,h::Real) = ∫(γ(h)*jump(∇(u) ⋅ n_Γg)*jump(∇(v) ⋅ n_Γg))dΓg - stiffness(t,u,v) = ∫(((β ∘ (velh,∇(φh))) ⋅ ∇(u)) * v)dΩ_bg + aₛ(u,v,h) + βh = β ∘ (velh,∇(φh)) + # dt = get_ode_solver(s).dt + # τ(β) = 1/(2sqrt((dt)^-2 + norm(β)^2/h^2)) + # # τ(β) = 0.5*(4/dt^2 + 4*norm(β)^2/h^2)^-0.5 # Based on MOOSE paper + # # τ(β) = h/(2norm(β)) + # τh = τ ∘ βh + # stiffness(t,u,v) = ∫((βh ⋅ ∇(u)) * v + (βh ⋅ ∇(u))*(τh*βh ⋅ ∇(v)))dΩ_bg #+ aₛ(u,v,h) + # mass(t, ∂ₜu, v) = ∫(∂ₜu * v + ∂ₜu * (τh*βh ⋅ ∇(v)))dΩ_bg + # forcing(t,v) = ∫(0v)dΩ_bg + + stiffness(t,u,v) = ∫((βh ⋅ ∇(u)) * v)dΩ_bg + aₛ(u,v,h) mass(t, ∂ₜu, v) = ∫(∂ₜu * v)dΩ_bg forcing(t,v) = ∫(0v)dΩ_bg + ∫(0*jump(∇(v) ⋅ n_Γg))dΓg # Second term is added to address the following issue: diff --git a/src/LevelSetEvolution/UnfittedEvolution/StabilisedReinit.jl b/src/LevelSetEvolution/UnfittedEvolution/StabilisedReinit.jl index f86f9c1..403c071 100644 --- a/src/LevelSetEvolution/UnfittedEvolution/StabilisedReinit.jl +++ b/src/LevelSetEvolution/UnfittedEvolution/StabilisedReinit.jl @@ -16,7 +16,7 @@ the artifical viscosity term with an interior jump penalty term. - `space::C`: FE space for level-set function - `assembler::Assembler`: Assembler for LS FE space - `params::E`: Tuple of Nitsche parameter `γd` and mesh size `h` -- `cache`: Cache for evolver, initially `nothing`. +- `cache`: Cache for reinitialiser, initially `nothing`. # Note - We expect the EmbeddedCollection `Ωs` to contain `:dΓ`. If this is not @@ -33,7 +33,7 @@ mutable struct StabilisedReinit{A,B,C,D} <: Reinitialiser cache function StabilisedReinit(V_φ::C,Ωs::EmbeddedCollection,dΩ_bg::B,h; γd = 20.0, - nls = NewtonSolver(LUSolver();maxiter=50,rtol=1.e-14,verbose=true), + nls = NewtonSolver(LUSolver();maxiter=10,rtol=1.e-14,verbose=true), assembler=SparseMatrixAssembler(V_φ,V_φ), stabilisation_method::A = InteriorPenalty(V_φ)) where {A,B,C} @@ -67,29 +67,41 @@ get_params(s::StabilisedReinit) = s.params get_element_diameters(s::StabilisedReinit) = s.params.h get_cache(s::StabilisedReinit) = s.cache -function solve!(s::StabilisedReinit,φh,nls_cache::Nothing) +function solve!(s::StabilisedReinit,φh,cache::Nothing) nls, V_φ, assembler, = s.nls, s.space, s.assembler + # Temp solution for later reinitialisation + φ = get_free_dof_values(φh); + φ_tmp = copy(φ) # Weak form res, jac = get_residual_and_jacobian(s,φh) # Operator and cache op = get_algebraic_operator(FEOperator(res,jac,V_φ,V_φ,assembler)) nls_cache = instantiate_caches(get_free_dof_values(φh),nls,op) - s.cache = nls_cache + s.cache = (;nls_cache,φh_tmp) # Solve solve!(get_free_dof_values(φh),nls,op,nls_cache) + copy!(φ_tmp,get_free_dof_values(φ)) update_collection!(s.Ωs,φh) # TODO: remove? return φh end -function solve!(s::StabilisedReinit,φh,nls_cache) +using GridapSolvers.SolverInterfaces: SOLVER_CONVERGED_ATOL,SOLVER_CONVERGED_RTOL,ConvergenceLog,finished_flag + +function solve!(s::StabilisedReinit,φh,cache) nls, V_φ, assembler, = s.nls, s.space, s.assembler + nls_cache, φ_tmp = cache + # Update φ_tmp + copy!(φ_tmp,get_free_dof_values(φh)) # Weak form res, jac = get_residual_and_jacobian(s,φh) # Operator and cache op = get_algebraic_operator(FEOperator(res,jac,V_φ,V_φ,assembler)) # Solve - solve!(get_free_dof_values(φh),nls,op,nls_cache) - update_collection!(s.Ωs,φh) # TODO: remove? + solve!(φ_tmp,nls,op,nls_cache) + if _get_solver_flag(nls.log) ∈ (SOLVER_CONVERGED_ATOL,SOLVER_CONVERGED_RTOL) + copy!(get_free_dof_values(φh),φ_tmp) + update_collection!(s.Ωs,φh) + end return φh end @@ -118,11 +130,12 @@ end struct InteriorPenalty <: StabilisationMethod dΛ + γg end -function InteriorPenalty(V_φ::FESpace) +function InteriorPenalty(V_φ::FESpace;γg=1.0) Λ = SkeletonTriangulation(get_triangulation(V_φ)) dΛ = Measure(Λ,2get_order(V_φ)) - return InteriorPenalty(dΛ) + return InteriorPenalty(dΛ,γg) end function get_residual_and_jacobian(s::StabilisedReinit{InteriorPenalty},φh) @@ -130,15 +143,49 @@ function get_residual_and_jacobian(s::StabilisedReinit{InteriorPenalty},φh) γd, h = s.params ϵ = 1e-20 dΛ = s.stabilisation_method.dΛ + γg = s.stabilisation_method.γg update_collection!(Ωs,φh) dΓ = Ωs.dΓ + γ(h) = γg*h^2 + + aₛ(u,v,h::CellField) = ∫(mean(γ ∘ h)*jump(∇(u)) ⋅ jump(∇(v)))dΛ + aₛ(u,v,h::Real) = ∫(γ(h)*jump(∇(u)) ⋅ jump(∇(v)))dΛ W(u,∇u) = sign(u) * ∇u / (ϵ + norm(∇u)) - a(w,u,v) = ∫(v*(W ∘ (w,∇(w))) ⋅ ∇(u))dΩ_bg + ∫(h*h*jump(∇(u)) ⋅ jump(∇(v)))dΛ + ∫((γd/h)*v*u)dΓ + a(w,u,v) = ∫(v*(W ∘ (w,∇(w))) ⋅ ∇(u))dΩ_bg + aₛ(u,v,h) + ∫((γd/h)*v*u)dΓ b(w,v) = ∫((sign ∘ w)*v)dΩ_bg res(u,v) = a(u,u,v) - b(u,v) jac(u,du,v) = a(u,du,v) # jac(u,du,v) = jacobian(res,[u,v],1) return res,jac +end + +struct MultiStageStabilisedReinit <: Reinitialiser + stages::Vector{StabilisedReinit} + function MultiStageStabilisedReinit(stages::Vector{<:StabilisedReinit}) + h = get_element_diameters(first(stages)) + for stage in stages + @check h === get_element_diameters(stage) + end + new(stages) + end +end + +get_cache(s::MultiStageStabilisedReinit) = get_cache.(s.stages) +get_element_diameters(s::MultiStageStabilisedReinit) = get_element_diameters(first(s.stages)) + +function solve!(s::MultiStageStabilisedReinit,φh,caches) + for (stage,cache) in zip(s.stages,caches) + solve!(stage,φh,cache) + end + return φh +end + +## Helper +function _get_solver_flag(log::ConvergenceLog) + r_abs = log.residuals[log.num_iters+1] + r_rel = r_abs / log.residuals[1] + flag = finished_flag(log.tols,log.num_iters,r_abs,r_rel) + return flag end \ No newline at end of file diff --git a/src/VelocityExtension_new.jl b/src/VelocityExtension_new.jl new file mode 100644 index 0000000..803cf53 --- /dev/null +++ b/src/VelocityExtension_new.jl @@ -0,0 +1,95 @@ +""" + abstract type AbstractVelocityExtension end + +An abstract type for velocity extension structures. Structs that inherit from + this type must implement the `project!` method. +""" +abstract type AbstractVelocityExtension end + +function project!(::AbstractVelocityExtension,::AbstractVector) + @abstractmethod +end + +project!(vel_ext::AbstractVelocityExtension,dF_vec::Vector{<:AbstractVector}) = broadcast(dF -> project!(vel_ext,dF),dF_vec) + +function Base.show(io::IO,object::AbstractVelocityExtension) + print(io,"$(nameof(typeof(object)))") +end + +""" + struct IdentityVelocityExtension <: AbstractVelocityExtension + +A velocity-extension method that does not perform any projection. +""" +struct IdentityVelocityExtension <: AbstractVelocityExtension end + +project!(::IdentityVelocityExtension,dF) = dF + +""" + struct VelocityExtension{A,B} <: AbstractVelocityExtension + +Wrapper to hold a stiffness matrix and a cache for +the Hilbertian extension-regularisation. See Allaire et al. 2022 +([link](https://doi.org/10.1016/bs.hna.2020.10.004)). + +The Hilbertian extension-regularisation method involves solving an +identification problem over a Hilbert space ``H`` on ``D`` with +inner product ``\\langle\\cdot,\\cdot\\rangle_H``: +*Find* ``g_\\Omega\\in H`` *such that* ``\\langle g_\\Omega,w\\rangle_H +=-J^{\\prime}(\\Omega)(w\\boldsymbol{n})~ +\\forall w\\in H.`` + +This provides two benefits: + 1) It naturally extends the shape sensitivity from ``\\partial\\Omega`` + onto the bounding domain ``D``; and + 2) ensures a descent direction for ``J(\\Omega)`` with additional regularity + (i.e., ``H`` as opposed to ``L^2(\\partial\\Omega)``) + +# Properties + +- `K::A`: The discretised inner product over ``H``. +- `cache::B`: Cached objects used for [`project!`](@ref) +""" +struct VelocityExtension{A,B} <: AbstractVelocityExtension + K :: A + cache :: B +end + +""" + VelocityExtension(biform,U_reg,V_reg;assem,ls) + +Create an instance of `VelocityExtension` given a bilinear form `biform`, +trial space `U_reg`, and test space `V_reg`. + +# Optional + +- `assem`: A matrix assembler +- `ls::LinearSolver`: A linear solver +""" +function VelocityExtension( + biform::Function, + U_reg::FESpace, + V_reg::FESpace; + assem = SparseMatrixAssembler(U_reg,V_reg), + ls::LinearSolver = LUSolver()) + ## Assembly + K = assemble_matrix(biform,assem,U_reg,V_reg) + ns = numerical_setup(symbolic_setup(ls,K),K) + x = allocate_in_domain(K) + cache = (ns,x) + return VelocityExtension(K,cache) +end + +""" + project!(vel_ext::VelocityExtension,dF::AbstractVector) -> dF + +Project shape derivative `dF` onto a function space described +by the `vel_ext`. +""" +function project!(vel_ext::VelocityExtension,dF::AbstractVector) + ns, x = vel_ext.cache + fill!(x,zero(eltype(x))) + solve!(x,ns,dF) + copy!(dF,x) + return dF +end \ No newline at end of file