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feat(mesh): add wedge facet connectivity maps
Extend facet-map machinery to `Wedge6`/`Wedge15` skeletons. - Add `Wedge6FacetMaps` builders aligned with topology reference numbering.
This commit is contained in:
Jukka Aho
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# This file is a part of JuliaFEM.
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# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
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using Tensors
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"""
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Wedge6FacetMaps
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Global edge and face ids on `Mesh{6, Wedge6}`: triangular faces use sorted
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3-tuples of vertex ids, quadrilateral faces use sorted 4-tuples (same idea as
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[`Tet4FacetMaps`](@ref) / [`Hex8FacetMaps`](@ref)).
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Fields match [`Hex8FacetMaps`](@ref): `elem_edge_gid` `(9, nelem)`,
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`elem_face_gid` `(5, nelem)`, orientation and fraction matrices.
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"""
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struct Wedge6FacetMaps <: AbstractFacetConnectivityMaps
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n_edges::Int
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n_faces::Int
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elem_edge_gid::Matrix{Int}
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elem_face_gid::Matrix{Int}
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elem_edge_orientation::Matrix{Int8}
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elem_face_orientation::Matrix{Int8}
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elem_edge_fraction::Matrix{Float64}
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elem_face_fraction::Matrix{Float64}
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end
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@inline function _wedge_sorted_face_triplet(conn::NTuple{6, UInt32}, verts::NTuple{3, Int})
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v = (conn[verts[1]], conn[verts[2]], conn[verts[3]])
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x = Int[v[1], v[2], v[3]]
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sort!(x)
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return (UInt32(x[1]), UInt32(x[2]), UInt32(x[3]))
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end
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@inline function _wedge_sorted_face_quad(conn::NTuple{6, UInt32}, verts::NTuple{4, Int})
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v = (conn[verts[1]], conn[verts[2]], conn[verts[3]], conn[verts[4]])
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x = Int[v[1], v[2], v[3], v[4]]
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sort!(x)
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return (UInt32(x[1]), UInt32(x[2]), UInt32(x[3]), UInt32(x[4]))
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end
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"""
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wedge_face_area_physical(X, local_face::Int) -> Float64
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Physical area of wedge face `local_face ∈ 1:5`: triangles use half the edge
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cross product norm; quads use the same two-triangle split as [`hex8_face_area_physical`](@ref).
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"""
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function wedge_face_area_physical(X::AbstractVector{V}, local_face::Int) where {V<:Vec{3}}
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fc = faces(Wedge6())[local_face]
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vs = fc.vertices
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n = length(vs)
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@inbounds p1 = X[vs[1]]
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@inbounds p2 = X[vs[2]]
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@inbounds p3 = X[vs[3]]
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if n == 3
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return 0.5 * norm((p2 - p1) × (p3 - p1))
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else
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@inbounds p4 = X[vs[4]]
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c1 = (p2 - p1) × (p3 - p1)
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c2 = (p3 - p1) × (p4 - p1)
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return 0.5 * (norm(c1) + norm(c2))
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end
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end
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"""
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wedge_edge_length_physical(X, local_edge::Int) -> Float64
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Edge length for `local_edge` in `edges(::Wedge6)` order, `X` length `6`.
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"""
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function wedge_edge_length_physical(X::AbstractVector{V}, local_edge::Int) where {V<:Vec{3}}
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ed = edges(Wedge6())[local_edge]
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i, j = ed.vertices
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@inbounds return norm(X[i] - X[j])
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end
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"""
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wedge_face_outward_sign(X, local_face::Int) -> Int8
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Compare face normal (triangle cross product or quad stub from first edges) with
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centroid-to-volume direction; `+1` when outward (same convention as tet/hex helpers).
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"""
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function wedge_face_outward_sign(X::AbstractVector{V}, local_face::Int) where {V<:Vec{3}}
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fc = faces(Wedge6())[local_face]
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vs = fc.vertices
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@inbounds ce = (X[1] + X[2] + X[3] + X[4] + X[5] + X[6]) / 6
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if length(vs) == 3
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@inbounds p1 = X[vs[1]]
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@inbounds p2 = X[vs[2]]
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@inbounds p3 = X[vs[3]]
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nvec = (p2 - p1) × (p3 - p1)
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cf = (p1 + p2 + p3) / 3
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else
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@inbounds p1 = X[vs[1]]
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@inbounds p2 = X[vs[2]]
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@inbounds p3 = X[vs[3]]
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@inbounds p4 = X[vs[4]]
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nvec = (p2 - p1) × (p3 - p1)
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cf = 0.25 * (p1 + p2 + p3 + p4)
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end
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s = dot(nvec, ce - cf)
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return s < 0 ? Int8(1) : Int8(-1)
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end
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@inline function _wedge6_element_coords(mesh::Mesh{6, Wedge6}, conn::NTuple{6, UInt32})
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return Vec{3, Float64}[mesh.nodes[Int(conn[i])] for i in 1:6]
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end
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"""
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build_wedge6_facet_maps(mesh::Mesh{6, Wedge6}) -> Wedge6FacetMaps
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"""
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function build_wedge6_facet_maps(mesh::Mesh{6, Wedge6})
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Ktop = Wedge6()
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edge_defs = edges(Ktop)
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face_defs = faces(Ktop)
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nelem = length(mesh.connectivity)
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edge_dict = Dict{Tuple{UInt32, UInt32}, Int}()
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tri_face_dict = Dict{NTuple{3, UInt32}, Int}()
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quad_face_dict = Dict{NTuple{4, UInt32}, Int}()
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elem_edge_gid = Matrix{Int}(undef, 9, nelem)
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elem_face_gid = Matrix{Int}(undef, 5, nelem)
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elem_edge_orientation = Matrix{Int8}(undef, 9, nelem)
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next_edge = 1
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next_face = 1
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@inbounds for eid in 1:nelem
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conn = mesh.connectivity[eid]
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for le in 1:9
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ed = edge_defs[le]
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i, j = ed.vertices
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ek = _sorted_edge_pair(conn[i], conn[j])
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gid = get(edge_dict, ek, nothing)
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if gid === nothing
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gid = next_edge
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edge_dict[ek] = gid
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next_edge += 1
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end
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elem_edge_gid[le, eid] = gid
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na = Int(conn[i])
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nb = Int(conn[j])
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elem_edge_orientation[le, eid] = na < nb ? Int8(1) : Int8(-1)
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end
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for lf in 1:5
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fc = face_defs[lf]
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fk = if length(fc.vertices) == 3
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_wedge_sorted_face_triplet(conn, fc.vertices)
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else
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_wedge_sorted_face_quad(conn, fc.vertices)
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end
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d = length(fc.vertices) == 3 ? tri_face_dict : quad_face_dict
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gid = get(d, fk, nothing)
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if gid === nothing
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gid = next_face
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d[fk] = gid
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next_face += 1
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end
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elem_face_gid[lf, eid] = gid
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end
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end
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n_edges = next_edge - 1
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n_faces = next_face - 1
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edge_touch = zeros(Int, n_edges)
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face_touch = zeros(Int, n_faces)
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@inbounds for eid in 1:nelem
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for le in 1:9
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edge_touch[elem_edge_gid[le, eid]] += 1
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end
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for lf in 1:5
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face_touch[elem_face_gid[lf, eid]] += 1
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end
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end
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elem_edge_fraction = Matrix{Float64}(undef, 9, nelem)
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elem_face_fraction = Matrix{Float64}(undef, 5, nelem)
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elem_face_orientation = Matrix{Int8}(undef, 5, nelem)
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@inbounds for eid in 1:nelem
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conn = mesh.connectivity[eid]
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X = _wedge6_element_coords(mesh, conn)
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for le in 1:9
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g = elem_edge_gid[le, eid]
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elem_edge_fraction[le, eid] = 1.0 / edge_touch[g]
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end
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for lf in 1:5
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g = elem_face_gid[lf, eid]
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elem_face_fraction[lf, eid] = 1.0 / face_touch[g]
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elem_face_orientation[lf, eid] = wedge_face_outward_sign(X, lf)
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end
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end
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return Wedge6FacetMaps(
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n_edges,
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n_faces,
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elem_edge_gid,
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elem_face_gid,
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elem_edge_orientation,
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elem_face_orientation,
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elem_edge_fraction,
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elem_face_fraction,
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)
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end
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"""
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wedge6_edge_orientation_sign(conn::NTuple{6,UInt32}, local_edge::Int) -> Int8
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Directed-edge hint matching [`build_wedge6_facet_maps`](@ref).
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"""
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function wedge6_edge_orientation_sign(conn::NTuple{6, UInt32}, local_edge::Int)
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ed = edges(Wedge6())[local_edge]
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va, vb = ed.vertices
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na = Int(conn[va])
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nb = Int(conn[vb])
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return na < nb ? Int8(1) : Int8(-1)
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end
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