From b30581ed82b2dc5d1120836b912df4c969cdcf5e Mon Sep 17 00:00:00 2001 From: Anne Boschman Date: Thu, 7 Nov 2024 11:29:06 +1100 Subject: [PATCH] added (non-working) canvas for div stab term --- bulk_ghost_penalty_canvas_div.jl | 749 +++++++++++++++++++++++++++++++ 1 file changed, 749 insertions(+) create mode 100644 bulk_ghost_penalty_canvas_div.jl diff --git a/bulk_ghost_penalty_canvas_div.jl b/bulk_ghost_penalty_canvas_div.jl new file mode 100644 index 0000000..d796f03 --- /dev/null +++ b/bulk_ghost_penalty_canvas_div.jl @@ -0,0 +1,749 @@ +using Gridap +using GridapEmbedded +using FillArrays +using LinearAlgebra + +include("BulkGhostPenaltyAssembleMaps.jl") + +# Manufactured solution +order = 0 +uex(x) = -VectorValue(2*x[1],2*x[2]) +pex(x) = (x[1]^2 + x[2]^2) +divuex(x) = -4.0 +# Select geometry +R = 0.2 +geom = disk(R, x0=Point(0.5,0.5)) + +# Setup background model +n=10 +partition = (n,n) +box = get_metadata(geom) +bgmodel = CartesianDiscreteModel((0,1,0,1),partition) +dp = box.pmax - box.pmin +h = dp[1]/n + +# Cut the background model with the mesh +cutdisk = cut(bgmodel,geom) + +# Compute mapping among background model +# cut cells and interior cells +strategy = AggregateAllCutCells() +aggregates = aggregate(strategy,cutdisk) + +""" + Creates an array of arrays with as many entries + as aggregates. For each aggregate, the array + contains the global cell IDs of that cells in the background + model that belong to the same aggregate + + TO-DO: with efficiency in mind we may want to store this + array of arrays as a Gridap.Arrays.Table. +""" +function setup_aggregate_to_cells(aggregates) + + size_aggregates=Dict{Int,Int}() + for (i,agg) in enumerate(aggregates) + if agg>0 + if !haskey(size_aggregates,agg) + size_aggregates[agg]=1 + else + size_aggregates[agg]+=1 + end + end + end + + touched=Dict{Int,Int}() + aggregate_to_cells=Vector{Vector{Int}}() + current_aggregate=1 + for (i,agg) in enumerate(aggregates) + if agg>0 + if (size_aggregates[agg]>1) + if !haskey(touched,agg) + push!(aggregate_to_cells,[i]) + touched[agg]=current_aggregate + current_aggregate+=1 + else + push!(aggregate_to_cells[touched[agg]],i) + end + end + end + end + aggregate_to_cells +end + +function setup_aggregates_bounding_box_model(bgmodel, aggregate_to_cells) + g=get_grid(bgmodel) + cell_coords=get_cell_coordinates(g) + D=num_dims(bgmodel) + xmin=Vector{Float64}(undef,D) + xmax=Vector{Float64}(undef,D) + + # Compute coordinates of the nodes defining the bounding boxes + bounding_box_node_coords= + Vector{Point{D,Float64}}(undef,length(aggregate_to_cells)*2^D) + ptr = [ (((i-1)*2^D)+1) for i in 1:length(aggregate_to_cells)+1 ] + data = collect(1:length(bounding_box_node_coords)) + bounding_box_node_ids = Gridap.Arrays.Table(data,ptr) + for (agg,cells) in enumerate(aggregate_to_cells) + p=first(cell_coords[cells[1]]) + for i in 1:D + xmin[i]=p[i] + xmax[i]=p[i] + end + for cell in cells + for p in cell_coords[cell] + for i in 1:D + xmin[i]=min(xmin[i],p[i]) + xmax[i]=max(xmax[i],p[i]) + end + end + end + bounds = [(xmin[i], xmax[i]) for i in 1:D] + point_iterator = Iterators.product(bounds...) + bounding_box_node_coords[bounding_box_node_ids[agg]] = + reshape([Point(p...) for p in point_iterator],2^D) + end + + # Set up the discrete model of bounding boxes + HEX_AXIS=1 + polytope=Polytope(Fill(HEX_AXIS,D)...) + scalar_reffe=ReferenceFE(polytope,lagrangian,Float64,1) + cell_types=fill(1,length(bounding_box_node_ids)) + cell_reffes=[scalar_reffe] + grid = Gridap.Geometry.UnstructuredGrid(bounding_box_node_coords, + bounding_box_node_ids, + cell_reffes, + cell_types, + Gridap.Geometry.Oriented()) + Gridap.Geometry.UnstructuredDiscreteModel(grid) +end + +aggregate_to_cells=setup_aggregate_to_cells(aggregates) +aggregates_bounding_box_model= + setup_aggregates_bounding_box_model(bgmodel,aggregate_to_cells) + +# colors = color_aggregates(aggregates,bgmodel) +# writevtk(Triangulation(bgmodel),"trian",celldata=["cellin"=>aggregates,"color"=>colors]) +# writevtk(aggregates_bounding_box_model, "bb_model") +# writevtk(bgmodel, "bg_model") + +""" + Changes the domain of a trial/test basis defined on + the reference space of bounding boxes to the reference + space of the agg cells + + TO-DO: in the future, for system of PDEs (MultiField) we should + also take care of blocks (BlockMap) +""" +function change_domain_bb_to_agg_cells(basis_bb, + ref_agg_cell_to_ref_bb_map, + Ωagg_cells, + agg_cells_to_aggregate) + @assert num_cells(Ωagg_cells)==length(ref_agg_cell_to_ref_bb_map) + @assert Gridap.CellData.DomainStyle(basis_bb)==ReferenceDomain() + bb_basis_style = Gridap.FESpaces.BasisStyle(basis_bb) + bb_basis_array = Gridap.CellData.get_data(basis_bb) + if (bb_basis_style==Gridap.FESpaces.TrialBasis()) + # Remove transpose map; we will add it later + @assert isa(bb_basis_array,Gridap.Arrays.LazyArray) + @assert isa(bb_basis_array.maps,Fill) + @assert isa(bb_basis_array.maps.value,typeof(transpose)) + bb_basis_array=bb_basis_array.args[1] + end + + bb_basis_array_to_Ωagg_cells_array = lazy_map(Reindex(bb_basis_array),agg_cells_to_aggregate) + bb_basis_array_to_Ωagg_cells_array = lazy_map(Broadcasting(∘), + bb_basis_array_to_Ωagg_cells_array, + ref_agg_cell_to_ref_bb_map) + if (bb_basis_style==Gridap.FESpaces.TrialBasis()) + # Add transpose + bb_basis_array_to_Ωagg_cells_array=lazy_map(transpose, bb_basis_array_to_Ωagg_cells_array) + end + + Gridap.CellData.GenericCellField(bb_basis_array_to_Ωagg_cells_array, + Ωagg_cells, + ReferenceDomain()) +end + + +# Set up objects required to compute both LHS and RHS of the L2 projection + +# Set up global spaces +Ωhact = Triangulation(cutdisk,ACTIVE) + +V = FESpace(Ωhact, ReferenceFE(raviart_thomas,Float64,order),conformity=:HDiv) +Q = FESpace(Ωhact, ReferenceFE(lagrangian,Float64,order), conformity=:L2) +U = TrialFESpace(V) +P = TrialFESpace(Q) +Y = MultiFieldFESpace([V, Q]) +X = MultiFieldFESpace([U, P]) + +# Generate an array with the global IDs of the cells +# that belong to an aggregrate. From now on, we will +# use the terminology "agg_cells" to refer to those +# cells of the background model that belong to an aggregate +# (i.e., they can be either cut or interior cells) +agg_cells=Vector{Int}() +for cells in aggregate_to_cells + append!(agg_cells,cells) +end + +# ref_agg_cell_to_agg_cell_map: \hat{K} -> K +Ω=Triangulation(bgmodel) +Ωagg_cells=view(Ω,agg_cells) +ref_agg_cell_to_agg_cell_map=get_cell_map(Ωagg_cells) + +# Generate an array that given the local ID of an "agg_cell" +# returns the ID of the aggregate to which it belongs +# (i.e., flattened version of aggregate_to_cells) +agg_cells_to_aggregate=Vector{Int}() +for (i,cells) in enumerate(aggregate_to_cells) + for _ in cells + push!(agg_cells_to_aggregate,i) + end +end + +# ref_agg_cell_to_ref_bb_map: \hat{K} -> K -> bb -> \hat{bb} +bb_to_ref_bb=lazy_map(Gridap.Fields.inverse_map,get_cell_map(aggregates_bounding_box_model)) +bb_to_ref_bb_agg_cells=lazy_map(Reindex(bb_to_ref_bb),agg_cells_to_aggregate) +ref_agg_cell_to_ref_bb_map= + lazy_map(Broadcasting(∘),bb_to_ref_bb_agg_cells,ref_agg_cell_to_agg_cell_map) + +# Compute LHS of L2 projection +degree=2*(order+1) +dΩagg_cells = Measure(Ωagg_cells,degree) +reffe =ReferenceFE(lagrangian,Float64,order) # Here we MUST use a Q space (not a P space!) +Qbb=FESpace(aggregates_bounding_box_model,reffe,conformity=:L2) # We need a DG space to represent the L2 projection +Pbb=TrialFESpace(Qbb) +pbb=get_trial_fe_basis(Pbb) +qbb=get_fe_basis(Qbb) + +reffe=ReferenceFE(raviart_thomas,Float64,order) +Vbb=FESpace(aggregates_bounding_box_model,reffe,conformity=:L2) +Ubb=TrialFESpace(Vbb) +ubb=get_trial_fe_basis(Ubb) +vbb=get_fe_basis(Vbb) + + +aggregate_to_local_cells=copy(aggregate_to_cells) +current_local_cell=1 +for (i,cells) in enumerate(aggregate_to_local_cells) + for j in 1:length(cells) + cells[j]=current_local_cell + current_local_cell+=1 + end +end + +function set_up_bulk_ghost_penalty_lhs(aggregates_bounding_box_model, + agg_cells_to_aggregate, + ref_agg_cell_to_ref_bb_map, + dΩagg_cells, + ubb, + vbb) + Ωagg_cells=dΩagg_cells.quad.trian + + # Change domain of vbb (test) from Ωbb to Ωagg_cells + vbb_Ωagg_cells=change_domain_bb_to_agg_cells(vbb, + ref_agg_cell_to_ref_bb_map, + Ωagg_cells, + agg_cells_to_aggregate) + + # Change domain of ubb (trial) from Ωbb to Ωagg_cells + ubb_Ωagg_cells=change_domain_bb_to_agg_cells(ubb, + ref_agg_cell_to_ref_bb_map, + Ωagg_cells, + agg_cells_to_aggregate) + + # Compute contributions to LHS of L2 projection + agg_cells_to_lhs_contribs=get_array(∫(vbb_Ωagg_cells⋅ubb_Ωagg_cells)dΩagg_cells) + + # Finally assemble LHS contributions + ass_lhs_map=BulkGhostPenaltyAssembleLhsMap(agg_cells_to_lhs_contribs) + lazy_map(ass_lhs_map,aggregate_to_local_cells) +end + +p_lhs=set_up_bulk_ghost_penalty_lhs(aggregates_bounding_box_model, + agg_cells_to_aggregate, + ref_agg_cell_to_ref_bb_map, + dΩagg_cells, + pbb, + qbb) + +u_lhs=set_up_bulk_ghost_penalty_lhs(aggregates_bounding_box_model, + agg_cells_to_aggregate, + ref_agg_cell_to_ref_bb_map, + dΩagg_cells, + ubb, + vbb) + +# Compute contributions to the RHS of the L2 projection +dx = get_trial_fe_basis(X) +dy = get_fe_basis(Y) +du,dp = dx +dv,dq = dy + +function _restrict_to_block(cell_dof_ids::Gridap.Arrays.LazyArray{<:Fill{<:Gridap.Fields.BlockMap}}, blockid) + map=cell_dof_ids.maps.value + @assert length(map.size)==1 + @assert blockid >= 1 + @assert blockid <= map.size[1] + cell_dof_ids.args[blockid] +end + +Ωagg_cell_dof_ids = get_cell_dof_ids(X,Ωagg_cells) +U_Ωagg_cell_dof_ids = _restrict_to_block(Ωagg_cell_dof_ids, 1) +P_Ωagg_cell_dof_ids = _restrict_to_block(Ωagg_cell_dof_ids, 2) +# Ωagg_cell_dof_ids[1][1] # cell 1, velo dof +# Ωagg_cell_dof_ids[1][2] # cell 1, pressure dofs + +### BEGIN TESTING CODE +# This code is just for testing purposes, so I have commented it out +# It allows to evaluate the LHS of the L2 projection corresponding to a +# particular FE function, instead of a basis +# uhex=interpolate(uex,Ustd) +# agg_cells_lhs_contribs_uhex=get_array(∫(vbb_Ωagg_cells*uhex)dΩagg_cells) +# ass_lhs_map_uhex=AssembleLhsMap(agg_cells_lhs_contribs_uhex) +# lhs_uhex=lazy_map(ass_lhs_map_uhex,aggregate_to_local_cells) +### END TESTING CODE + +function compute_agg_cells_local_dof_ids(agg_cells_dof_ids, aggregate_to_agg_cells) + agg_cells_local_dof_ids=copy(agg_cells_dof_ids) + current_cell=1 + for agg_cells in aggregate_to_agg_cells + g2l=Dict{Int32,Int32}() + current_local_dof=1 + for (i,_) in enumerate(agg_cells) + current_cell_dof_ids=agg_cells_dof_ids[current_cell] + for (j, dof) in enumerate(current_cell_dof_ids) + if !(dof in keys(g2l)) + g2l[dof]=current_local_dof + agg_cells_local_dof_ids[current_cell][j]=current_local_dof + current_local_dof+=1 + else + agg_cells_local_dof_ids[current_cell][j]=g2l[dof] + end + end + current_cell+=1 + println(agg_cells_local_dof_ids) + end + end + agg_cells_local_dof_ids +end + +U_agg_cells_local_dof_ids= + compute_agg_cells_local_dof_ids(U_Ωagg_cell_dof_ids, aggregate_to_local_cells) +P_agg_cells_local_dof_ids= + compute_agg_cells_local_dof_ids(P_Ωagg_cell_dof_ids, aggregate_to_local_cells) + + +function set_up_h_U(aggregates_bounding_box_model, + agg_cells_to_aggregate, + Ωagg_cells) + degree = 0 # We are integrating a constant function + # Thus, degree=0 is enough for exact integration + Ωbb = Triangulation(aggregates_bounding_box_model) + dΩbb = Measure(Ωbb, degree) + h_U_array = get_array(∫(1.0)dΩbb) + h_U_array = lazy_map(Reindex(h_U_array), agg_cells_to_aggregate) + CellField(h_U_array, Ωagg_cells) +end + + +function compute_aggregate_dof_ids(agg_cells_dof_ids, aggregate_to_agg_cells) + aggregate_dof_ids=Vector{Vector{Int}}(undef, length(aggregate_to_agg_cells)) + current_aggregate=1 + current_cell=1 + for agg_cells in aggregate_to_agg_cells + current_aggregate_dof_ids=Int[] + for (i,_) in enumerate(agg_cells) + current_cell_dof_ids=agg_cells_dof_ids[current_cell] + for (j, dof) in enumerate(current_cell_dof_ids) + if !(dof in current_aggregate_dof_ids) + push!(current_aggregate_dof_ids, dof) + end + end + current_cell+=1 + end + aggregate_dof_ids[current_aggregate]=current_aggregate_dof_ids + current_aggregate+=1 + end + aggregate_dof_ids +end + +function _get_single_field_fe_basis(a::Gridap.MultiField.MultiFieldFEBasisComponent) + a.single_field +end +function _get_single_field_fe_basis(a) + a +end +function _is_multifield_fe_basis_component(a::Gridap.MultiField.MultiFieldFEBasisComponent) + true +end +function _is_multifield_fe_basis_component(a) + false +end +function _nfields(a::Gridap.MultiField.MultiFieldFEBasisComponent) + a.nfields +end +function _fieldid(a::Gridap.MultiField.MultiFieldFEBasisComponent) + a.fieldid +end + +""" + dv, du: Test and trial basis functions. They may be components of a MultiFieldCellField + + # Compute and assemble the bulk penalty stabilization term + # ∫( (dv-dv_l2_proj_agg_cells)*(du-du_l2_proj_agg_cells))*dΩ_agg_cells (long version) + # ∫( (dv)*(du-du_l2_proj_agg_cells))*dΩ_agg_cells (simplified, equivalent version) +""" +function interior_bulk_penalty_stabilization_collect_cell_matrix(agg_cells_to_aggregate, + ref_agg_cell_to_ref_bb_map, + dΩagg_cells, + dv, # Test basis + du, # Trial basis (to project) + dvbb, # Bounding box space test basis + lhs, + Ωagg_cell_dof_ids, + agg_cells_local_dof_ids, + agg_cells_to_aggregate_dof_ids, + h_U, + γ) + + + Ωagg_cells=dΩagg_cells.quad.trian + + # Change domain of vbb (test) from Ωbb to Ωagg_cells + dvbb_Ωagg_cells=change_domain_bb_to_agg_cells(dvbb, + ref_agg_cell_to_ref_bb_map, + Ωagg_cells, + agg_cells_to_aggregate) + + du_single_field=_get_single_field_fe_basis(du) + agg_cells_rhs_contribs=get_array(∫(dvbb_Ωagg_cells⋅du_single_field)dΩagg_cells) + ass_rhs_map=BulkGhostPenaltyAssembleRhsMap(agg_cells_local_dof_ids,agg_cells_rhs_contribs) + rhs=lazy_map(ass_rhs_map,aggregate_to_local_cells) + + # TO-DO: optimize using our own optimized version Gridap.Fields.Map + # of backslash that re-uses storage for lu factors among cells, etc. + dv_l2_proj_bb_dofs=lazy_map(\,lhs,rhs) + + # Generate bb-wise array of fields. For each aggregate's bounding box, + # it provides the l2 projection of all basis functions in du + # restricted to the cells included in the bounding box of the aggregate + dv_l2_proj_bb_array=lazy_map(Gridap.Fields.linear_combination, + dv_l2_proj_bb_dofs, + Gridap.CellData.get_data(dvbb)) + + # # Change domain of dv_l2_proj_bb_array from bb to agg_cells + dv_l2_proj_bb_array_agg_cells=lazy_map(Broadcasting(∘), + lazy_map(Reindex(dv_l2_proj_bb_array),agg_cells_to_aggregate), + ref_agg_cell_to_ref_bb_map) + + du_l2_proj_bb_array_agg_cells=lazy_map(transpose, dv_l2_proj_bb_array_agg_cells) + + if (_is_multifield_fe_basis_component(du)) + @assert _is_multifield_fe_basis_component(dv) + @assert _nfields(du)==_nfields(dv) + nfields=_nfields(du) + fieldid=_fieldid(du) + du_l2_proj_bb_array_agg_cells=lazy_map( + Gridap.Fields.BlockMap((1,nfields),fieldid), + du_l2_proj_bb_array_agg_cells) + end + + du_l2_proj_agg_cells = Gridap.CellData.GenericCellField(du_l2_proj_bb_array_agg_cells, + dΩagg_cells.quad.trian, + ReferenceDomain()) + + # Manually set up the arrays that collect_cell_matrix would return automatically + w = [] + r = [] + c = [] + + dv_du_mat_contribs=get_array(∫(γ*dv⋅du)*dΩagg_cells) + if (_is_multifield_fe_basis_component(dv)) + nfields=_nfields(dv) + fieldid=_fieldid(dv) + Ωagg_cell_dof_ids=lazy_map(Gridap.Fields.BlockMap(nfields,fieldid),Ωagg_cell_dof_ids) + end + push!(w, dv_du_mat_contribs) + push!(r, Ωagg_cell_dof_ids) + push!(c, Ωagg_cell_dof_ids) + + # In the MultiField case, I have had to add this change domain + # call before setting up the term right below. Otherwise, we get an error + # when trying to multiply the fields. Not sure why this is happening + dvΩagg_cells=Gridap.CellData.change_domain(dv,Ωagg_cells,ReferenceDomain()) + + proj_dv_du_mat_contribs=get_array(∫(γ*(-1.0)*dvΩagg_cells⋅(du_l2_proj_agg_cells))*dΩagg_cells) + + if (_is_multifield_fe_basis_component(du)) + nfields=_nfields(du) + fieldid=_fieldid(du) + agg_cells_to_aggregate_dof_ids= + lazy_map(Gridap.Fields.BlockMap(nfields,fieldid),agg_cells_to_aggregate_dof_ids) + end + + push!(w, proj_dv_du_mat_contribs) + push!(r, Ωagg_cell_dof_ids) + push!(c, agg_cells_to_aggregate_dof_ids) + + w, r, c +end + +U_aggregate_dof_ids=compute_aggregate_dof_ids(U_Ωagg_cell_dof_ids,aggregate_to_cells) +U_agg_cells_to_aggregate_dof_ids=lazy_map(Reindex(U_aggregate_dof_ids),agg_cells_to_aggregate) + +P_aggregate_dof_ids=compute_aggregate_dof_ids(P_Ωagg_cell_dof_ids,aggregate_to_cells) +P_agg_cells_to_aggregate_dof_ids=lazy_map(Reindex(P_aggregate_dof_ids),agg_cells_to_aggregate) + +γ = 10.0 # Interior bulk-penalty stabilization parameter + # (@amartinhuertas no idea what a reasonable value is) + +h_U = set_up_h_U(aggregates_bounding_box_model, agg_cells_to_aggregate, Ωagg_cells) + +# Manually set up the arrays that collect_cell_matrix would return automatically +wp,rp,cp=interior_bulk_penalty_stabilization_collect_cell_matrix(agg_cells_to_aggregate, + ref_agg_cell_to_ref_bb_map, + dΩagg_cells, + dq, # Test basis + dp, # Trial basis (to project) + qbb, # Bounding box space test basis + p_lhs, + P_Ωagg_cell_dof_ids, + P_agg_cells_local_dof_ids, + P_agg_cells_to_aggregate_dof_ids, + h_U, + γ) + +wu,ru,cu=interior_bulk_penalty_stabilization_collect_cell_matrix(agg_cells_to_aggregate, + ref_agg_cell_to_ref_bb_map, + dΩagg_cells, + dv, # Test basis + du, # Trial basis (to project) + vbb, # Bounding box space test basis + u_lhs, + U_Ωagg_cell_dof_ids, + U_agg_cells_local_dof_ids, + U_agg_cells_to_aggregate_dof_ids, + h_U, + γ) + +Ωcut = Triangulation(cutdisk,PHYSICAL) +dΩcut = Measure(Ωcut,degree) +# # Set up global projection matrix +# Ωcut = Triangulation(cutdisk,PHYSICAL) +# dΩcut = Measure(Ωcut,degree) +# a_nodiv((u,p),(v,q))=∫(v⋅u+q*p)dΩcut +# wrc_nodiv=Gridap.FESpaces.collect_cell_matrix(X,Y,a_nodiv(dx,dy)) + +# assem_nodiv=SparseMatrixAssembler(X,Y) +# Anostab_nodiv=assemble_matrix(assem_nodiv, wrc_nodiv) +# cond(Array(Anostab_nodiv)) + +# # Add the bulk penalty stabilization term to wrc_nodiv +# push!(wrc_nodiv[1], wp...) +# push!(wrc_nodiv[2], rp...) +# push!(wrc_nodiv[3], cp...) + +# push!(wrc_nodiv[1], wu...) +# push!(wrc_nodiv[2], ru...) +# push!(wrc_nodiv[3], cu...) + +# Awithstab_nodiv=assemble_matrix(assem_nodiv, wrc_nodiv) +# cond(Array(Awithstab_nodiv)) + +# # Set up rhs global projection +# l_nodiv((v,q))=∫(v⋅uex+q*pex)dΩcut +# b_nodiv = assemble_vector(l_nodiv, Y) + +# global_l2_proj_dofs_nodiv = Awithstab_nodiv\b_nodiv +# xh_nodiv = FEFunction(X, global_l2_proj_dofs_nodiv) +# uh_nodiv,ph_nodiv = xh_nodiv + +# euh_nodiv = uex-uh_nodiv +# # @assert sum(∫(euh_nodiv⋅euh_nodiv)*dΩcut) < 1.0e-12 + +# eph_nodiv = pex-ph_nodiv +# # @assert sum(∫(eph_nodiv*eph_nodiv)*dΩcut) < 1.0e-12 +# eph_nodiv_norm = sum(∫(eph_nodiv*eph_nodiv)*dΩcut) +# euh_nodiv_norm = sum(∫(euh_nodiv⋅euh_nodiv)*dΩcut) +# # k=0 yields eph = 0.00012 and euh = 5.5e-30 +# edivuh_nodiv = divuex-(∇⋅uh_nodiv) +# edivuh_nodiv_norm = sum(∫(edivuh_nodiv⋅edivuh_nodiv)*dΩcut) + +## TEST 1 +a((u,p),(v,q))=∫(v⋅u+q*p+(∇⋅u)*(∇⋅v))dΩcut +wrc=Gridap.FESpaces.collect_cell_matrix(X,Y,a(dx,dy)) + +assem=SparseMatrixAssembler(X,Y) +Anostab=assemble_matrix(assem, wrc) +cond_nostab = cond(Array(Anostab)) + +# Set up rhs global projection +l((v,q))=∫(v⋅uex+q*pex+(∇⋅v)*divuex)dΩcut +b = assemble_vector(l, Y) + +## NO STABILIZATION +if cond_nostab<1e35 + global_l2_proj_dofs_nostab = Anostab\b + xh_nostab = FEFunction(X, global_l2_proj_dofs_nostab) + uh_nostab,ph_nostab = xh_nostab + euh_nostab = uex-uh_nostab + eph_nostab = pex-ph_nostab + edivuh_nostab = divuex-(∇⋅uh_nostab) + norm_euh_nostab = sum(∫(euh_nostab⋅euh_nostab)*dΩcut) + norm_eph_nostab = sum(∫(eph_nostab*eph_nostab)*dΩcut) + edivuh_nostab = sum(∫(edivuh_nostab⋅edivuh_nostab)*dΩcut) +else + println("Singular exception is raised as error when solving the system (as cond= $cond_nostab is high?)") +end +# k=0 yields euh = 1.2e-32, eph = 0.00017, edivuh = 6.8e-30, κ= 3.15e32 +# k=0 yields euh = ?, eph = ?, edivuh = ?, κ= 4.3e36 + +## U + P STABILIZATION +# Add the bulk penalty stabilization terms for u and p to wrc +push!(wrc[1], wp...) +push!(wrc[2], rp...) +push!(wrc[3], cp...) + +push!(wrc[1], wu...) +push!(wrc[2], ru...) +push!(wrc[3], cu...) + +# Check the condition number when only the p and u stabilization terms are included. +Aupstab=assemble_matrix(assem, wrc) +cond_upstab = cond(Array(Aupstab)) + +# CHECK errors when only the p and u stabilization terms are included. +global_l2_proj_dofs_upstab = Aupstab\b +xh_upstab = FEFunction(X, global_l2_proj_dofs_upstab) +uh_upstab,ph_upstab = xh_upstab +euh_upstab = uex-uh_upstab +eph_upstab = pex-ph_upstab +edivuh_upstab = divuex-(∇⋅uh_upstab) +norm_euh_upstab = sum(∫(euh_upstab⋅euh_upstab)*dΩcut) +norm_eph_upstab = sum(∫(eph_upstab*eph_upstab)*dΩcut) +norm_edivuh_upstab = sum(∫(edivuh_upstab⋅edivuh_upstab)*dΩcut) +# k=0 yields euh = 6.3e-31, eph = 0.00055, edivuh = 2.4e-28, κ= 11492 +# k=2 yields euh = 5.3e-22, eph = 3.0e-18, edivuh = 3.0e-18, κ= 1.7e11 + +## +DIVU STABILIZATION +## Compute ∫( (div_dv)*(div_du-div_du_l2_proj_agg_cells))*dΩ_agg_cells (simplified, equivalent version) +# Manually set up the arrays that collect_cell_matrix would return automatically +w_divu = [] +r_divu = [] +c_divu = [] + +## (I) Let's set up the div_dv_div_du_mat_contribs (first part of the integral, that is ∫( (div_dv)*(div_du)*dΩ_agg_cells +div_dv_div_du_mat_contribs=get_array(∫(γ*(∇⋅dv)⋅(∇⋅du))*dΩagg_cells) +U_Ωagg_cell_dof_ids = _restrict_to_block(Ωagg_cell_dof_ids, 1) +if (_is_multifield_fe_basis_component(dv)) + nfields=_nfields(dv) + fieldid=_fieldid(dv) + U_Ωagg_cell_dof_ids=lazy_map(Gridap.Fields.BlockMap(nfields,fieldid),U_Ωagg_cell_dof_ids) +end + +push!(w_divu, div_dv_div_du_mat_contribs) +push!(r_divu, U_Ωagg_cell_dof_ids) +push!(c_divu, U_Ωagg_cell_dof_ids) + +## Set up ∫( (div_dv)*(-div_du_l2_proj_agg_cells))*dΩ_agg_cells +div_dv=∇⋅(_get_single_field_fe_basis(dv)) +pdofs=Gridap.FESpaces.get_fe_dof_basis(P) +div_dv_pdofs_values=pdofs(div_dv) +div_dv_in_pressure_space_cell_array=lazy_map(Gridap.Fields.linear_combination, + div_dv_pdofs_values, + Gridap.CellData.get_data(_get_single_field_fe_basis(dq))) +div_dv_in_pressure_space_single_field= Gridap.FESpaces.SingleFieldFEBasis(div_dv_in_pressure_space_cell_array, + get_triangulation(P), + Gridap.FESpaces.TestBasis(), + Gridap.CellData.ReferenceDomain()) +div_dv_in_pressure_space=Gridap.MultiField.MultiFieldFEBasisComponent(div_dv_in_pressure_space_single_field,1,2) + +div_du_in_pressure_space_cell_array=lazy_map(transpose,div_dv_in_pressure_space_cell_array) +div_du_in_pressure_space_single_field=Gridap.FESpaces.SingleFieldFEBasis(div_du_in_pressure_space_cell_array, + get_triangulation(P), + Gridap.FESpaces.TrialBasis(), + Gridap.CellData.ReferenceDomain()) +div_du_in_pressure_space=Gridap.MultiField.MultiFieldFEBasisComponent(div_du_in_pressure_space_single_field,1,2) + +div_dv_div_du_in_pressure_space_mat_contribs=get_array(∫(γ*div_dv_in_pressure_space⋅div_du_in_pressure_space)*dΩagg_cells) #not sure if neccesary? +div_dv_div_du_mat_contribs ≈ div_dv_div_du_in_pressure_space_mat_contribs + +### Compute Π_Q_bb(div_du) +dqbb_Ωagg_cells =change_domain_bb_to_agg_cells(qbb,ref_agg_cell_to_ref_bb_map,Ωagg_cells,agg_cells_to_aggregate) +agg_cells_rhs_contribs=get_array(∫(dqbb_Ωagg_cells⋅div_du_in_pressure_space_single_field)dΩagg_cells) +# agg_cells_rhs_contribs[1] +ass_rhs_map=BulkGhostPenaltyAssembleRhsMap(P_agg_cells_local_dof_ids,agg_cells_rhs_contribs) +rhs=lazy_map(ass_rhs_map,aggregate_to_local_cells) +div_dv_l2_proj_bb_dofs=lazy_map(\,p_lhs,rhs) + +# Generate bb-wise array of fields. For each aggregate's bounding box, + # it provides the l2 projection of all basis functions in dp + # restricted to the cells included in the bounding box of the aggregate +div_dv_l2_proj_bb_array=lazy_map(Gridap.Fields.linear_combination, + div_dv_l2_proj_bb_dofs, + Gridap.CellData.get_data(qbb)) + +div_dv_l2_proj_bb_array_agg_cells=lazy_map(Broadcasting(∘), + lazy_map(Reindex(div_dv_l2_proj_bb_array),agg_cells_to_aggregate), + ref_agg_cell_to_ref_bb_map) + +div_du_l2_proj_bb_array_agg_cells=lazy_map(transpose, div_dv_l2_proj_bb_array_agg_cells) + +if (_is_multifield_fe_basis_component(dp)) + @assert _is_multifield_fe_basis_component(dq) + @assert _nfields(dp)==_nfields(dq) + nfields=_nfields(dp) + fieldid=_fieldid(dp) + div_du_l2_proj_bb_array_agg_cells=lazy_map( + Gridap.Fields.BlockMap((1,nfields),fieldid), + div_du_l2_proj_bb_array_agg_cells) +end + +div_du_l2_proj_agg_cells = Gridap.CellData.GenericCellField(div_du_l2_proj_bb_array_agg_cells, dΩagg_cells.quad.trian,ReferenceDomain()) + +# In the MultiField case, I have had to add this change domain +# call before setting up the term right below. Otherwise, we get an error +# when trying to multiply the fields. Not sure why this is happening +# dv_Ωagg_cells=Gridap.CellData.change_domain(dv,Ωagg_cells,ReferenceDomain()) +div_dv_Ωagg_cells=Gridap.CellData.change_domain(∇⋅dv,Ωagg_cells,ReferenceDomain()) + +proj_div_dv_div_du_mat_contribs=get_array(∫(γ*(-1.0)*div_dv_Ωagg_cells*(div_du_l2_proj_agg_cells))*dΩagg_cells) + +P_Ωagg_cell_dof_ids = _restrict_to_block(Ωagg_cell_dof_ids, 2) +P_aggregate_dof_ids=compute_aggregate_dof_ids(P_Ωagg_cell_dof_ids,aggregate_to_cells) +P_agg_cells_to_aggregate_dof_ids=lazy_map(Reindex(P_aggregate_dof_ids),agg_cells_to_aggregate) + +if (_is_multifield_fe_basis_component(dp)) + nfields=_nfields(dp) + fieldid=_fieldid(dp) + P_agg_cells_to_aggregate_dof_ids= + lazy_map(Gridap.Fields.BlockMap(nfields,fieldid),P_agg_cells_to_aggregate_dof_ids) +end + +push!(w_divu, proj_div_dv_div_du_mat_contribs) +push!(r_divu, U_Ωagg_cell_dof_ids) # test +push!(c_divu, P_agg_cells_to_aggregate_dof_ids) # trial + +## Now add div stabilization to A +push!(wrc[1], w_divu...) +push!(wrc[2], r_divu...) +push!(wrc[3], c_divu...) + +# Assembly +Awithstab=assemble_matrix(assem, wrc) +cond_withstab = cond(Array(Awithstab)) + +global_l2_proj_dofs_withstab = Awithstab\b +xh_withstab = FEFunction(X, global_l2_proj_dofs_withstab) +uh_withstab,ph_withstab = xh_withstab +euh_withstab = uex-uh_withstab +eph_withstab = pex-ph_withstab +edivuh_withstab = divuex-(∇⋅uh_withstab) +norm_euh_withstab = sum(∫(euh_withstab⋅euh_withstab)*dΩcut) +norm_eph_withstab = sum(∫(eph_withstab*eph_withstab)*dΩcut) +norm_edivuh_withstab = sum(∫(edivuh_withstab⋅edivuh_withstab)*dΩcut) +# k=0 yields euh = 0.0014, eph = 0.47, edivuh = 0.47, κ= 8.51e11 +# k=2 yields euh = 0.00013, eph = 0.088, edivuh = 0.088, κ= 2.9e14 \ No newline at end of file