p4est datastructures #780

koehlerson · 2023-07-31T15:14:40Z

to be discussed at FerriteCon 23, register now: https://ferrite-fem.github.io/FerriteCon/

TODO

Followup PRs

DofHandler integration
Transfer of solution vector between dof handlers
make it work for arbitrary polynomial order
error estimation
- faster local ZZ error estimator
- Kelly error estimator
- Dörfler marking https://www.ams.org/journals/mcom/2020-89-326/S0025-5718-2020-03553-4/S0025-5718-2020-03553-4.pdf
iterators
- cell
- face
- edge
- vertex
conformization

…nd corner_neighbor need tests

…hanges. should be correct imho

…x corresponds to child_id

…pping

…corner and edge neighbor

termi-official · 2024-06-11T11:05:10Z

1. Why doesn't `Ferrite.refine!` include `Ferrite.balanceforest!(grid)`? (Of course, internally it makes sense to have these separated, but I would have assumed that the API function `refine!` would do both.

There is a performance trap hiding here. Users might refine single elements one by one and if this triggers rebalancing the refinement can become quickly very expensive. Hence the users is responsible to call the balance function once he is done.

4. [..] I guess at least some old to new cells mapping is required to do this efficiently?

Yes, that is missing and necessary for any time-dependent problem. We add more features later (see follow-up PRs). This PR concentrates on the core implementation with documentation.

Error Estimation
Note that this is up the the user to implement? (If it is, I just assume here).

Here we run into the issue that Ferrite is "too low-level". The majority of error estimators need direct access to an evaluation of the energy or flux. So for now the only option is that the packages on top of Ferrite provide these.

termi-official · 2024-06-11T11:05:50Z

src/Dofs/DofHandler.jl

+    # Maps from entity to dofs
+    # `vertexdict` keeps track of the visited vertices. The first dof added to vertex v is
+    # stored in vertexdict[v].
+    vertexdicts::Vector{Vector{Int}}
+    # `edgedict` keeps track of the visited edges, this will only be used for a 3D problem.
+    # An edge is uniquely determined by two global vertices, with global direction going
+    # from low to high vertex number.
+    edgedicts::Vector{Dict{Tuple{Int,Int}, Int}}
+    # `facedict` keeps track of the visited faces. We only need to store the first dof we
+    # add to the face since currently more dofs per face isn't supported. In
+    # 2D a face (i.e. a line) is uniquely determined by 2 vertices, and in 3D a face (i.e. a
+    # surface) is uniquely determined by 3 vertices.
+    facedicts::Vector{Dict{NTuple{3,Int}, Int}}


Reminder to me: Try to remove this again.

koehlerson · 2024-06-11T11:07:57Z

I assumed it doesn't follow the AbstractGrid interface, otherwise you could have used that directly in the DofHandler I assumed. If it is, would be nice to document what it does include and what it doesn't from the interface.

It fulfills the AbstractGrid interface, but the problem is that the AbstractCell interface is too strict for adaptive/distributed grids (cells respectively). Thus, the DofHandler fails in distributing dofs, because of calls like

Ferrite.jl/src/Dofs/DofHandler.jl

Line 522 in 3ae61fa

for (vi, vertex) in pairs(vertices(cell))

which assume that a cell knows about its global vertex ids, which isn't the case for the OctantBWG cells. Even the OctreeBWG won't know about its global ids, instead given o::OctantBWG in some tree::OctreeBWG part of forest::ForestBWG you can determine o's global vertex ids. I think it's the same with distributed but just one layer removed and instead you can imagine to track the shared dofs somehow

Yeah for the algorithm or interface in general I need to discuss with @termi-official a bit.

koehlerson · 2024-06-11T11:19:22Z

@fredrikekre what do you think in terms of minimal abstraction for gauss point data which eases state variable transfer and error estimation vs giving it up to the user to do this?

KnutAM · 2024-06-11T13:24:29Z

There is a performance trap hiding here. Users might refine single elements one by one and if this triggers rebalancing the refinement can become quickly very expensive. Hence the users is responsible to call the balance function once he is done.

OK, if the intention is that you should be able to call refine! for one cell at a time, and then do balance, then let's leave that to later than. I thought the interface refine!(grid, cell_numbers::Vector) was intended as a single step refine all cells.

I guess we can at some point introduce a new function remesh that does refine + balance for P4est AMR and only refine for e.g. "triangle-splitting" AMR. But to not take the namespace (going into 1.0), wouldn't it make sense to call this refine_tree or smth since the split is specific to P4est?

KnutAM · 2024-06-11T13:24:40Z

Side-note that I discovered when trying to understand the above:
I think users could be surprised that refine!(grid, cellids) is not equivalent to

for cellid in cellids
    refine!(grid, cellid)
end

Perhaps the refine!(grid, ::Int) should be an internal function to encourage users to always use a collection of cells to refine?

fredrikekre · 2024-06-11T14:17:43Z

Because the first call generates new cell numbers or?

koehlerson · 2024-06-11T19:14:59Z

Because the first call generates new cell numbers or?

Yes, as soon as the integer dispatch is called 4 (2D) or 8 (3D) new cells are inserted therefore shifting the cellids of the other cells

koehlerson · 2024-06-12T07:50:16Z

I guess we can at some point introduce a new function remesh that does refine + balance for P4est AMR and only refine for e.g. "triangle-splitting" AMR. But to not take the namespace (going into 1.0), wouldn't it make sense to call this refine_tree or smth since the split is specific to P4est?

I'd vote for structs that act as a flag whether or not after refinement should be balanced. That should be okay for all approaches. Balancing is not something super tightly connected to p4est. It's useful in cases where you don't want nested non-conformity constraints. I would rather go for refine since more or less every adaptive approach can be seen as a tree approach (also triangle splitting)

KnutAM · 2024-06-12T07:59:00Z

I'd vote for structs that act as a flag whether or not after refinement should be balanced.

That sounds good to me!

fredrikekre · 2024-06-12T08:08:22Z

@fredrikekre what do you think in terms of minimal abstraction for gauss point data which eases state variable transfer and error estimation vs giving it up to the user to do this?

No idea, but I guess there have to be some way to transfer things between the meshes, also the solution, right? A good start would probably be to have a cellmapping and then you can interpolate as you wish for quadrature data perhaps?

…at makes actual sense

koehlerson · 2024-06-13T10:52:59Z

@fredrikekre what do you think in terms of minimal abstraction for gauss point data which eases state variable transfer and error estimation vs giving it up to the user to do this?

No idea, but I guess there have to be some way to transfer things between the meshes, also the solution, right? A good start would probably be to have a cellmapping and then you can interpolate as you wish for quadrature data perhaps?

Yes the solution transfer is not so problematic since we have the knowledge about the fields, their underlying interpolation and the previous grid they lived on. However, what about the Gauss point data, e.g. internal variables. We need to transfer those as well in the long run. Further, we also need some interface for stress/flux computation since most error estimator do something with the stress/flux. If its just linear elastic, then it's simple you can just have a function somehow, but what about the case with internal variables? I think dealii also doesn't have a solution to it, since they only provide the kelly estimator for the poisson problem AFAIU https://www.dealii.org/current/doxygen/deal.II/classKellyErrorEstimator.html

fredrikekre · 2024-06-13T11:07:25Z

Yea at least for internal variables I don't think there is a good default solution so you would just have to provide the information for users to do it in a way that fits the problem at hand.

termi-official · 2024-06-13T11:42:07Z

Yea at least for internal variables I don't think there is a good default solution so you would just have to provide the information for users to do it in a way that fits the problem at hand.

xref Nonlinear Finite Elements (Ch 8.6.2) by Wriggers

bplcn · 2024-06-14T04:56:20Z

I tried to construct a mapping dictionary of the cell ids from a old grid/forest to the new one for 2D grid.

function cell_id_map(forest_old::f, forest_new::f) where f
    
    cell_id_old = 0
    cell_id_new = 0

    cellid_old2new_Dict = Dict()

    for (ktree, tree) in enumerate(forest_old.cells)
        kleaf_new = 1

        for kleaf in 1:length(tree.leaves)
            
            cell_id_old += 1

            if forest_old.cells[ktree].leaves[kleaf].l == forest_new.cells[ktree].leaves[kleaf_new].l
                # the element is not refine  
                cell_id_new += 1
                cellid_old2new_Dict[cell_id_old] = [cell_id_new]
                kleaf_new += 1
            else 
                # refined
                cellid_old2new_Dict[cell_id_old] = [cell_id_new+1, cell_id_new+2, cell_id_new+3, cell_id_new+4]
                cell_id_new += 4
                kleaf_new += 4
            end
        end
    end
    return cellid_old2new_Dict
end

For each time of refinement, the old element may split or not change. Thus the values in the dictionary is a vector contain one or four elements. The implementation compares the old and new forest. Thus both of them should be stored.

koehlerson · 2024-06-14T09:21:32Z

I tried to construct a mapping dictionary of the cell ids from a old grid/forest to the new one for 2D grid.

function cell_id_map(forest_old::f, forest_new::f) where f
    
    cell_id_old = 0
    cell_id_new = 0

    cellid_old2new_Dict = Dict()

    for (ktree, tree) in enumerate(forest_old.cells)
        kleaf_new = 1

        for kleaf in 1:length(tree.leaves)
            
            cell_id_old += 1

            if forest_old.cells[ktree].leaves[kleaf].l == forest_new.cells[ktree].leaves[kleaf_new].l
                # the element is not refine  
                cell_id_new += 1
                cellid_old2new_Dict[cell_id_old] = [cell_id_new]
                kleaf_new += 1
            else 
                # refined
                cellid_old2new_Dict[cell_id_old] = [cell_id_new+1, cell_id_new+2, cell_id_new+3, cell_id_new+4]
                cell_id_new += 4
                kleaf_new += 4
            end
        end
    end
    return cellid_old2new_Dict
end

For each time of refinement, the old element may split or not change. Thus the values in the dictionary is a vector contain one or four elements. The implementation compares the old and new forest. Thus both of them should be stored.

Cool thanks! That's a good starting point. You should consider making PRs 🚀

koehlerson · 2024-06-14T11:54:49Z

I tried to construct a mapping dictionary of the cell ids from a old grid/forest to the new one for 2D grid.

function cell_id_map(forest_old::f, forest_new::f) where f
    
    cell_id_old = 0
    cell_id_new = 0

    cellid_old2new_Dict = Dict()

    for (ktree, tree) in enumerate(forest_old.cells)
        kleaf_new = 1

        for kleaf in 1:length(tree.leaves)
            
            cell_id_old += 1

            if forest_old.cells[ktree].leaves[kleaf].l == forest_new.cells[ktree].leaves[kleaf_new].l
                # the element is not refine  
                cell_id_new += 1
                cellid_old2new_Dict[cell_id_old] = [cell_id_new]
                kleaf_new += 1
            else 
                # refined
                cellid_old2new_Dict[cell_id_old] = [cell_id_new+1, cell_id_new+2, cell_id_new+3, cell_id_new+4]
                cell_id_new += 4
                kleaf_new += 4
            end
        end
    end
    return cellid_old2new_Dict
end

For each time of refinement, the old element may split or not change. Thus the values in the dictionary is a vector contain one or four elements. The implementation compares the old and new forest. Thus both of them should be stored.

We have to think about how we can construct the mapping without having two instantiated ForestBWGs so either we have refine! functions that alter some mapping struct as e.g. your dict and then we forward it to refine! and balance! or we have to return the mappings from the functions

termi-official · 2024-06-14T14:05:07Z

Thanks @bplcn !

I tried to construct a mapping dictionary of the cell ids from a old grid/forest to the new one for 2D grid.
function cell_id_map(forest_old::f, forest_new::f) where f
    
    cell_id_old = 0
    cell_id_new = 0

    cellid_old2new_Dict = Dict()

    for (ktree, tree) in enumerate(forest_old.cells)
        kleaf_new = 1

        for kleaf in 1:length(tree.leaves)
            
            cell_id_old += 1

            if forest_old.cells[ktree].leaves[kleaf].l == forest_new.cells[ktree].leaves[kleaf_new].l
                # the element is not refine  
                cell_id_new += 1
                cellid_old2new_Dict[cell_id_old] = [cell_id_new]
                kleaf_new += 1
            else 
                # refined
                cellid_old2new_Dict[cell_id_old] = [cell_id_new+1, cell_id_new+2, cell_id_new+3, cell_id_new+4]
                cell_id_new += 4
                kleaf_new += 4
            end
        end
    end
    return cellid_old2new_Dict
end
For each time of refinement, the old element may split or not change. Thus the values in the dictionary is a vector contain one or four elements. The implementation compares the old and new forest. Thus both of them should be stored.
We have to think about how we can construct the mapping without having two instantiated ForestBWGs so either we have refine! functions that alter some mapping struct as e.g. your dict and then we forward it to refine! and balance! or we have to return the mappings from the functions

This is similar to what I had in mind.

amr_map = initialize_amr_map(forest, instanced_grid)
refine!(forest, elements_to_refine, amr_map)
coarsen!(forest, elements_to_coarsen, amr_map)
balance!(forest, amp_map)

where we can now query all refinement and coarsening information through amr_map.

fredrikekre · 2024-06-14T14:47:47Z

refine!(forest, elements_to_refine, amr_map)
coarsen!(forest, elements_to_coarsen, amr_map)

This would have the same problem as #780 (comment)? Need to refine and coarsen in a single call instead?

termi-official · 2024-06-14T15:06:46Z

refine!(forest, elements_to_refine, amr_map)
coarsen!(forest, elements_to_coarsen, amr_map)
This would have the same problem as #780 (comment)? Need to refine and coarsen in a single call instead?

Indeed. This was just a sketch assuming that we have all indices properly determined a-priori. In general the loop body is a bit more involved

build leaf mesh
setup problem on leaf mesh
solve problem
estimate error
mark cells
refine marked cells
balance
build leaf mesh
setup problem on leaf mesh
solve problem
estimate error again
mark cells with the error estimate
coarsen marked cells
balance again
if not converged goto 1

And now you can have different variations of

We could also provide a function

enum WatDo
   Coarsen
   Refine
   Keep
end
elements_to_adapt = Vector{WatDo}(...)
adapt_mesh!(forest, elements_to_adapt, amr_map)

termi-official · 2024-06-17T15:56:30Z

Found 2 more issues in 3D with Maxi. Last commit has test coverage for them.

Not all hanging nodes are detected.
For rotated elements the unique node detection fails.

termi-official · 2024-06-17T16:02:09Z

Failing analytical example:

using Ferrite, FerriteGmsh, SparseArrays

const ref_geometry = RefHexahedron
const geometry_type = Hexahedron
const sdim = 3

grid = generate_grid(geometry_type, ntuple(_->4, sdim));

function random_deformation_field(x::Vec{dim}) where dim
    if any(x .≈ -1.0) || any(x .≈ 1.0)
        return x
    else
        Vec{dim}(x .+ (rand(dim).-0.5)*0.1)
    end
end
transform_coordinates!(grid, random_deformation_field)
grid  = ForestBWG(grid,10)

analytical_solution(x) = atan(2*(norm(x)-0.5)/0.02)
analytical_rhs(x) = -laplace(analytical_solution,x)

function assemble_cell!(ke, fe, cellvalues, ue, coords)
    fill!(ke, 0.0)
    fill!(fe, 0.0)

    n_basefuncs = getnbasefunctions(cellvalues)
    for q_point in 1:getnquadpoints(cellvalues)
        x = spatial_coordinate(cellvalues, q_point, coords)
        dΩ = getdetJdV(cellvalues, q_point)
        for i in 1:n_basefuncs
            Nᵢ = shape_value(cellvalues, q_point, i)
            ∇Nᵢ = shape_gradient(cellvalues, q_point, i)
            fe[i] += analytical_rhs(x) * Nᵢ * dΩ
            for j in 1:n_basefuncs
                ∇Nⱼ = shape_gradient(cellvalues, q_point, j)
                ke[i, j] += ∇Nⱼ ⋅ ∇Nᵢ * dΩ
            end
        end
    end
end

function assemble_global!(K, f, a, dh, cellvalues)
    ## Allocate the element stiffness matrix and element force vector
    n_basefuncs = getnbasefunctions(cellvalues)
    ke = zeros(n_basefuncs, n_basefuncs)
    fe = zeros(n_basefuncs)
    ## Create an assembler
    assembler = start_assemble(K, f)
    ## Loop over all cells
    for cell in CellIterator(dh)
        reinit!(cellvalues, cell)
        @views ue = a[celldofs(cell)]
        ## Compute element contribution
        coords = getcoordinates(cell)
        assemble_cell!(ke, fe, cellvalues, ue, coords)
        ## Assemble ke and fe into K and f
        assemble!(assembler, celldofs(cell), ke, fe)
    end
    return K, f
end

function solve(grid)
    dim = 3
    order = 1
    ip = Lagrange{ref_geometry, order}()
    qr = QuadratureRule{ref_geometry}(2)
    cellvalues = CellValues(qr, ip);

    dh = DofHandler(grid)
    add!(dh, :u, ip)
    close!(dh);

    ch = ConstraintHandler(dh)
    add!(ch, ConformityConstraint(:u))
    add!(ch, Dirichlet(:u, getfacetset(grid, "top"), (x, t) -> 0.0))
    add!(ch, Dirichlet(:u, getfacetset(grid, "right"), (x, t) -> 0.0))
    add!(ch, Dirichlet(:u, getfacetset(grid, "left"), (x, t) -> 0.0))
    add!(ch, Dirichlet(:u, getfacetset(grid, "bottom"), (x, t) -> 0.0))
    close!(ch);

    K = create_sparsity_pattern(dh,ch)
    f = zeros(ndofs(dh))
    a = zeros(ndofs(dh))
    assemble_global!(K, f, a, dh, cellvalues);
    apply!(K, f, ch)
    u = K \ f;
    apply!(u,ch)
    return u,dh,ch,cellvalues
end

function solve_adaptive(initial_grid::ForestBWG{sdim}) where sdim
    ip = Lagrange{ref_geometry, 1}()
    qr_sc = QuadratureRule{ref_geometry}(2)
    cellvalues = CellValues(qr_sc, ip);
    finished = false
    i = 1
    grid = deepcopy(initial_grid)
    pvd = VTKFileCollection("heat_amr.pvd",grid);
    while !finished && i<=10
        @show i
        transfered_grid = Ferrite.creategrid(grid)
        u,dh,ch,cv = solve(transfered_grid)
        # σ_gp, σ_gp_sc = compute_fluxes(u,dh)
        # projector = L2Projector(Lagrange{ref_geometry, 1}(), transfered_grid)
        # σ_dof = project(projector, σ_gp, QuadratureRule{ref_geometry}(2))
        cells_to_refine = Int[]
        error_arr = Float64[]
        for (cellid,cell) in enumerate(CellIterator(dh))
            reinit!(cellvalues, cell)
            @views ue = u[celldofs(cell)]
            error = 0.0
            for q_point in 1:getnquadpoints(cellvalues)
                x = spatial_coordinate(cv, q_point, getcoordinates(cell))
                dΩ = getdetJdV(cellvalues,q_point)
                error += abs(analytical_solution(x) - function_value(cellvalues, q_point, ue)) * dΩ
            end
            if error > 0.001
                push!(cells_to_refine,cellid)
            end
            push!(error_arr,error)
        end

        addstep!(pvd, i, dh) do vtk
            write_solution(vtk, dh, u)
            # write_projection(vtk, projector, σ_dof, "flux")
            # write_cell_data(vtk, getindex.(collect(Iterators.flatten(σ_gp_sc)),1), "flux sc x")
            # write_cell_data(vtk, getindex.(collect(Iterators.flatten(σ_gp_sc)),2), "flux sc y")
            write_cell_data(vtk, error_arr, "error")
        end

        Ferrite.refine!(grid, cells_to_refine)
        Ferrite.balanceforest!(grid)

        i += 1
        if isempty(cells_to_refine)
            finished = true
        end
    end
    close(pvd);
    transfered_grid = Ferrite.creategrid(grid)
    u,dh,ch,cv = solve(transfered_grid)
end

u,dh,ch,cv = solve_adaptive(grid)

koehlerson added 30 commits August 2, 2021 18:56

add lookup tables and helper functions

6c830d7

clean up and tests for lookup

b47f930

added parent and child_id

294b463

change to UInt8

61fba0e

fixed parent and included child_id for 2d case

bbcac4d

fixed parent and included child_id for 2d case

3c51d2c

add check in parent for root node, added test for that

e4486cb

add some comment about child_id ordering

a60ef58

further test

e827fa4

added descendants, face edge and corner_neighbor, descendants, edge a…

81290c4

…nd corner_neighbor need tests

shifted morton index by 1 and included morton index constructor tests

689997b

include TODOs

5ceba3f

proper docstrings

e70bf11

AssertionError in test for morton index constructor

44d4c98

fixed descendants, need to wait for zulip responds to confirm those c…

e33d859

…hanges. should be correct imho

I think I have found a bug in tests and in child_id, now morton inde…

98d8ac0

…x corresponds to child_id

fix 2d version of child_id, added tests with child_id morton index ma…

5944c57

…pping

fixed edge neighbor, included 2D corner neighbor, included tests for …

fa2509c

…corner and edge neighbor

maxlevel always last arg with default value based on Burstedde et al.

99f2fc6

started adaptive grid

517b6a6

corner neighborhood for 2D

17f145f

face neighbor for 2D

621c091

topology for 3D

96c9392

Merge branch 'master' into mk/adaptivehex

4871b45

cleanup topology from the past

d352bb3

Merge branch 'master' into mk/p4est

a4a6d89

add constructor for Octree and Forest

13c994f

maximumsize of octant

4201ab9

start of refine, not fully working yet

af61a76

Merge branch 'master' into mk/p4est

834936f

termi-official reviewed Jun 11, 2024

View reviewed changes

change qr for error estimator in elasticity example

bc1db41

resolve reported bug by adjusting the nrefcells logic to something th…

c746834

…at makes actual sense

[skip ci] test coverage for failing MWEs in 3D

b7492cf

termi-official and others added 5 commits June 18, 2024 12:55

Derp

d50665d

typo in hanging nodes; doesn't resolve bug

8461ed6

failing example; something fishy in the conformity info

30a3b36

Fix shared edge node detection.

9b38d62

heat_adaptivity 3D version for debugging

b913af4

Provide feedback

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p4est datastructures #780

p4est datastructures #780

koehlerson commented Jul 31, 2023 •

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termi-official commented Jun 17, 2024

p4est datastructures #780

Are you sure you want to change the base?

p4est datastructures #780

Conversation

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TODO

Followup PRs

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