From c8add0befa53cf42ae34ff9c3948a740de8ea00a Mon Sep 17 00:00:00 2001
From: Jukka Aho <ahojukka5@gmail.com>
Date: Sat, 9 May 2026 16:30:36 +0300
Subject: [PATCH] feat(src): add packed_layout.jl

src/assemblers/packed_layout.jl | 597 ++++++++++++++++++++++++++++++++++++++++  1 file changed, 597 insertions(+)
---
 src/assemblers/packed_layout.jl | 597 ++++++++++++++++++++++++++++++++
 1 file changed, 597 insertions(+)
 create mode 100644 src/assemblers/packed_layout.jl

diff --git a/src/assemblers/packed_layout.jl b/src/assemblers/packed_layout.jl
new file mode 100644
index 0000000..2308f2e
--- /dev/null
+++ b/src/assemblers/packed_layout.jl
@@ -0,0 +1,597 @@
+# This file is a part of JuliaFEM.
+# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
+
+# Per-partition packed DOF vectors: owned block + ghost block, maps to global DOFs.
+
+"""
+    mark_matvec_stencil_closure!(
+        closure::BitVector, owned::BitVector, elements, dof_connectivity::DOFConnectivity) -> closure
+
+[`fill!`](@ref)`(closure, false)` then, for every global DOF `i` with `owned[i]`,
+mark all global DOFs belonging to **any** element incident on `i` (same fan-in
+as one row of [`apply_K!`](@ref)).
+
+`length(closure) == length(owned) == dof_connectivity.n_total_dofs`. Allocation-free
+given buffers (partitioning / Krylov outer setup, not first call after `fill!`).
+"""
+function mark_matvec_stencil_closure!(
+    closure::BitVector,
+    owned::BitVector,
+    elements::AbstractVector{El},
+    dof_connectivity::DOFConnectivity,
+) where {El <: Element}
+    nd = dof_connectivity.n_total_dofs
+    length(closure) == nd ||
+        throw(DimensionMismatch("closure length $(length(closure)), n_total_dofs $nd"))
+    length(owned) == nd ||
+        throw(DimensionMismatch("owned length $(length(owned)), n_total_dofs $nd"))
+    isempty(elements) && throw(ArgumentError("elements must be non-empty"))
+
+    fill!(closure, false)
+    dte = dof_connectivity.dof_to_elements
+    @inbounds for dof_i in 1:nd
+        owned[dof_i] || continue
+        conns = dte[dof_i]
+        for cidx in 1:length(conns)
+            conn = conns[cidx]
+            ev = elem_id(conn)
+            elem = elements[ev]
+            for d in element_dofs(elem)
+                closure[Int(d)] = true
+            end
+        end
+    end
+    return closure
+end
+
+"""
+    PartitionPackedLayout
+
+Per-partition layout for a replicated global DOF vector (`ndofs_global`).
+
+Packed storage order is **owned DOFs first** (increasing global index), then
+**ghost DOFs** (increasing global index). Ghosts are `closure \\ owned` where
+`closure` is either an element-patch reference (see
+[`build_partition_packed_layout`](@ref)`(handler, …)`) or a matvec row stencil
+(see [`build_partition_packed_layout_for_matvec`](@ref)); both use
+[`ghost_dof_mask!`](@ref).
+
+# Fields
+- `part` — partition id
+- `ndofs_global` — global vector length
+- `n_owned`, `n_packed` — owned count and `n_owned + n_ghost`
+- `packed_to_global[k]` — global DOF index for packed slot `k`
+- `global_to_packed[g]` — packed slot for global `g`, or `0` if outside this patch
+- `owned_rows` — length `ndofs_global` bit mask; true on owned DOFs (for
+  [`apply_K_owned_rows!`](@ref))
+
+Use [`build_partition_packed_layout`](@ref) (element-patch ghosts, MPI halo
+lists) or [`build_partition_packed_layout_for_matvec`](@ref) (row stencil
+closure). Setup allocates; gather / expand are allocation-free given existing
+buffers.
+"""
+struct PartitionPackedLayout
+    part::Int
+    ndofs_global::Int
+    n_owned::Int
+    n_packed::Int
+    packed_to_global::Vector{Int}
+    global_to_packed::Vector{Int}
+    owned_rows::BitVector
+end
+
+function _assert_disjoint_owned_ghost(owned::BitVector, ghost::BitVector)
+    length(owned) == length(ghost) ||
+        throw(DimensionMismatch("owned length $(length(owned)), ghost $(length(ghost))"))
+    @inbounds for i in eachindex(owned)
+        (owned[i] & ghost[i]) &&
+            throw(ArgumentError("owned and ghost masks overlap at global DOF index $i"))
+    end
+    return nothing
+end
+
+"""
+    build_partition_packed_layout(part, owned::BitVector, ghost::BitVector)
+        -> PartitionPackedLayout
+
+`length(owned) == length(ghost) == ndofs_global`. Masks must be disjoint;
+ghosts are typically `ghost_dof_mask!(…, referenced, owned)`.
+
+Allocates the returned struct and copies `owned` into `layout.owned_rows`.
+"""
+function build_partition_packed_layout(
+    part::Int,
+    owned::BitVector,
+    ghost::BitVector,
+)::PartitionPackedLayout
+    _assert_disjoint_owned_ghost(owned, ghost)
+    nd = length(owned)
+    buf_own = Vector{Int}(undef, nd)
+    buf_gh = Vector{Int}(undef, nd)
+    n_own = collect_true_indices!(buf_own, owned)
+    n_gh = collect_true_indices!(buf_gh, ghost)
+    n_packed = n_own + n_gh
+    p2g = Vector{Int}(undef, n_packed)
+    @inbounds for k in 1:n_own
+        p2g[k] = buf_own[k]
+    end
+    @inbounds for k in 1:n_gh
+        p2g[n_own + k] = buf_gh[k]
+    end
+    g2p = zeros(Int, nd)
+    @inbounds for k in 1:n_packed
+        g = p2g[k]
+        g2p[g] = k
+    end
+    return PartitionPackedLayout(part, nd, n_own, n_packed, p2g, g2p, copy(owned))
+end
+
+"""
+    build_partition_packed_layout(
+        handler, layout, mesh, node_owner, elements, part::Int) -> PartitionPackedLayout
+
+Setup helper: same owned / referenced / ghost convention as
+[`build_rank_halo_exchanges`](@ref). Ghosts are DOFs on **this part's volume
+elements** that are not owned here (MPI element-part halo). For a matrix-free
+matvec on each part, prefer [`build_partition_packed_layout_for_matvec`](@ref).
+
+Allocates temporary masks each call (partitioning setup, not a Krylov inner loop).
+"""
+function build_partition_packed_layout(
+    handler::DOFHandler,
+    layout::MeshPartitionLayout,
+    mesh::AbstractMesh,
+    node_owner::Vector{Int},
+    elements::AbstractVector{El},
+    part::Int,
+) where {El <: Element}
+    validate_partition(layout, length(elements))
+    ndofs = handler.total_dofs
+    ep = element_indices_for_part(layout, part)
+    owned = falses(ndofs)
+    mark_owned_vertex_field_dofs!(owned, handler, node_owner, part)
+    ref = falses(ndofs)
+    mark_referenced_dofs!(ref, elements, ep, ndofs)
+    ghost = falses(ndofs)
+    ghost_dof_mask!(ghost, ref, owned)
+    return build_partition_packed_layout(part, owned, ghost)
+end
+
+"""
+    build_partition_packed_layout_for_matvec(
+        handler, layout, mesh, node_owner, elements, part, dof_connectivity)
+            -> PartitionPackedLayout
+
+Like [`build_partition_packed_layout`](@ref)`(handler, layout, …, part)`, but the
+referenced set is the **row stencil closure** from
+[`mark_matvec_stencil_closure!`](@ref) instead of volume elements on this part
+only. Ghosts then cover every DOF needed for [`apply_K_owned_rows!`](@ref) on
+this partition, so (gather → expand → matvec → sum owned rows) matches a
+replicated global [`apply_K!`](@ref) up to floating-point roundoff.
+
+Allocates temporary masks each call (setup, not an inner Krylov iteration).
+"""
+function build_partition_packed_layout_for_matvec(
+    handler::DOFHandler,
+    layout::MeshPartitionLayout,
+    mesh::AbstractMesh,
+    node_owner::Vector{Int},
+    elements::AbstractVector{El},
+    part::Int,
+    dof_connectivity::DOFConnectivity,
+) where {El <: Element}
+    validate_partition(layout, length(elements))
+    ndofs = handler.total_dofs
+    dof_connectivity.n_total_dofs == ndofs ||
+        throw(DimensionMismatch(
+            "dof_connectivity.n_total_dofs $(dof_connectivity.n_total_dofs) != handler.total_dofs $ndofs",
+        ))
+
+    owned = falses(ndofs)
+    mark_owned_vertex_field_dofs!(owned, handler, node_owner, part)
+    closure = falses(ndofs)
+    mark_matvec_stencil_closure!(closure, owned, elements, dof_connectivity)
+    ghost = falses(ndofs)
+    ghost_dof_mask!(ghost, closure, owned)
+    return build_partition_packed_layout(part, owned, ghost)
+end
+
+"""
+    build_matvec_halo_exchanges(handler, layout, mesh, node_owner, elements, dof_connectivity)
+        -> Vector{RankHaloExchange}
+
+Same partition adjacency and send/recv pairing as [`build_rank_halo_exchanges`](@ref),
+but each part's ghost mask is `closure \\ owned` where `closure` comes from
+[`mark_matvec_stencil_closure!`](@ref) (identical to ghosts in
+[`build_partition_packed_layout_for_matvec`](@ref)).
+
+Together with that packed layout, [`unpack_halo_recv_to_packed!`](@ref) fills every
+ghost slot after MPI receives. Setup-only (allocates).
+"""
+function build_matvec_halo_exchanges(
+    handler::DOFHandler,
+    layout::MeshPartitionLayout,
+    mesh::Mesh{N, T},
+    node_owner::Vector{Int},
+    elements::AbstractVector{El},
+    dof_connectivity::DOFConnectivity,
+) where {N, T, El <: Element}
+    validate_partition(layout, length(mesh.connectivity))
+    ndofs = handler.total_dofs
+    dof_connectivity.n_total_dofs == ndofs ||
+        throw(DimensionMismatch(
+            "dof_connectivity.n_total_dofs $(dof_connectivity.n_total_dofs) != handler.total_dofs $ndofs",
+        ))
+    np = maximum(layout.element_part_id)
+    length(node_owner) == length(mesh.nodes) ||
+        throw(DimensionMismatch("node_owner length $(length(node_owner)), nnodes $(length(mesh.nodes))"))
+
+    adj = build_partition_adjacency(layout, mesh)
+
+    owned = Vector{BitVector}(undef, np)
+    ghost = Vector{BitVector}(undef, np)
+    closure_tmp = falses(ndofs)
+    @inbounds for p in 1:np
+        owned[p] = falses(ndofs)
+        mark_owned_vertex_field_dofs!(owned[p], handler, node_owner, p)
+        mark_matvec_stencil_closure!(closure_tmp, owned[p], elements, dof_connectivity)
+        ghost[p] = falses(ndofs)
+        ghost_dof_mask!(ghost[p], closure_tmp, owned[p])
+    end
+
+    tmp = falses(ndofs)
+    dof_buf = Vector{Int}(undef, ndofs)
+
+    exchanges = Vector{RankHaloExchange}(undef, np)
+    @inbounds for p in 1:np
+        recv_n = Int[]
+        recv_d = Vector{Int}[]
+        send_n = Int[]
+        send_d = Vector{Int}[]
+        for q in adj.neighbors[p]
+            _mask_intersect!(tmp, ghost[p], owned[q])
+            nloc = collect_true_indices!(dof_buf, tmp)
+            push!(recv_n, q)
+            push!(recv_d, collect(Int, view(dof_buf, 1:nloc)))
+        end
+        for q in adj.neighbors[p]
+            _mask_intersect!(tmp, ghost[q], owned[p])
+            nloc = collect_true_indices!(dof_buf, tmp)
+            push!(send_n, q)
+            push!(send_d, collect(Int, view(dof_buf, 1:nloc)))
+        end
+        exchanges[p] = RankHaloExchange(p, recv_n, recv_d, send_n, send_d)
+    end
+
+    return exchanges
+end
+
+"""
+    gather_from_global_to_packed!(packed, x_global, layout) -> packed
+
+`length(packed) ≥ layout.n_packed`, `length(x_global) ≥ layout.ndofs_global`.
+
+For each packed slot `k`, `packed[k] = x_global[packed_to_global[k]]`.
+
+Allocation-free.
+"""
+function gather_from_global_to_packed!(
+    packed::AbstractVector{Float64},
+    x_global::AbstractVector{Float64},
+    layout::PartitionPackedLayout,
+)
+    n = layout.n_packed
+    length(packed) ≥ n ||
+        throw(DimensionMismatch("packed length $(length(packed)) < n_packed $n"))
+    length(x_global) ≥ layout.ndofs_global ||
+        throw(DimensionMismatch("x_global length $(length(x_global)) < ndofs_global $(layout.ndofs_global)"))
+    p2g = layout.packed_to_global
+    @inbounds for k in 1:n
+        packed[k] = x_global[p2g[k]]
+    end
+    return packed
+end
+
+"""
+    expand_packed_to_global!(x_global, packed, layout) -> x_global
+
+Writes `x_global[g] = packed[k]` for each mapping `g = packed_to_global[k]`.
+Entries outside the patch are **not** modified.
+
+Allocation-free.
+"""
+function expand_packed_to_global!(
+    x_global::AbstractVector{Float64},
+    packed::AbstractVector{Float64},
+    layout::PartitionPackedLayout,
+)
+    n = layout.n_packed
+    length(packed) ≥ n ||
+        throw(DimensionMismatch("packed length $(length(packed)) < n_packed $n"))
+    length(x_global) ≥ layout.ndofs_global ||
+        throw(DimensionMismatch("x_global length $(length(x_global)) < ndofs_global $(layout.ndofs_global)"))
+    p2g = layout.packed_to_global
+    @inbounds for k in 1:n
+        x_global[p2g[k]] = packed[k]
+    end
+    return x_global
+end
+
+"""
+    gather_owned_from_global_to_packed!(packed, x_global, layout) -> packed
+
+Fills only the **owned** prefix `packed[1:layout.n_owned]` from `x_global`
+(increasing global DOF order, matching [`build_partition_packed_layout`](@ref)).
+Ghost slots `packed[layout.n_owned+1:end]` are not touched.
+
+Allocation-free.
+"""
+function gather_owned_from_global_to_packed!(
+    packed::AbstractVector{Float64},
+    x_global::AbstractVector{Float64},
+    layout::PartitionPackedLayout,
+)
+    no = layout.n_owned
+    length(packed) ≥ no ||
+        throw(DimensionMismatch("packed length $(length(packed)) < n_owned $no"))
+    length(x_global) ≥ layout.ndofs_global ||
+        throw(DimensionMismatch("x_global length $(length(x_global)) < ndofs_global $(layout.ndofs_global)"))
+    p2g = layout.packed_to_global
+    @inbounds for k in 1:no
+        packed[k] = x_global[p2g[k]]
+    end
+    return packed
+end
+
+"""
+    copy_owned_subset_to_packed_owned_prefix!(packed, v_owned, layout) -> packed
+
+Write `packed[k] = v_owned[k]` for `k = 1:layout.n_owned`. Ghost slots are not modified.
+
+`length(v_owned) == layout.n_owned`. Matches lean Krylov storage keyed by the owned prefix of
+[`packed_to_global`](@ref).
+
+Allocation-free.
+"""
+function copy_owned_subset_to_packed_owned_prefix!(
+    packed::AbstractVector{Float64},
+    v_owned::AbstractVector{Float64},
+    layout::PartitionPackedLayout,
+)
+    no = layout.n_owned
+    length(v_owned) == no ||
+        throw(DimensionMismatch("v_owned length $(length(v_owned)), n_owned $no"))
+    length(packed) ≥ no ||
+        throw(DimensionMismatch("packed length $(length(packed)) < n_owned $no"))
+    @inbounds for k in 1:no
+        packed[k] = v_owned[k]
+    end
+    return packed
+end
+
+"""
+    extract_owned_subset_from_global!(v_owned, x_global, layout) -> v_owned
+
+`v_owned[k] = x_global[packed_to_global[k]]` for `k = 1:layout.n_owned`.
+
+Allocation-free.
+"""
+function extract_owned_subset_from_global!(
+    v_owned::AbstractVector{Float64},
+    x_global::AbstractVector{Float64},
+    layout::PartitionPackedLayout,
+)
+    no = layout.n_owned
+    length(v_owned) == no ||
+        throw(DimensionMismatch("v_owned length $(length(v_owned)), n_owned $no"))
+    length(x_global) ≥ layout.ndofs_global ||
+        throw(DimensionMismatch(
+            "x_global length $(length(x_global)) < ndofs_global $(layout.ndofs_global)",
+        ))
+    p2g = layout.packed_to_global
+    @inbounds for k in 1:no
+        v_owned[k] = x_global[p2g[k]]
+    end
+    return v_owned
+end
+
+"""
+    gather_owned_rows_from_workspace!(v_owned, y_workspace, layout) -> v_owned
+
+`v_owned[k] = y_workspace[packed_to_global[k]]` after e.g. [`apply_K_owned_rows!`](@ref)
+(which leaves non-owned rows at zero).
+
+Allocation-free.
+"""
+function gather_owned_rows_from_workspace!(
+    v_owned::AbstractVector{Float64},
+    y_workspace::AbstractVector{Float64},
+    layout::PartitionPackedLayout,
+)
+    no = layout.n_owned
+    nd = layout.ndofs_global
+    length(v_owned) == no ||
+        throw(DimensionMismatch("v_owned length $(length(v_owned)), n_owned $no"))
+    length(y_workspace) ≥ nd ||
+        throw(DimensionMismatch(
+            "y_workspace length $(length(y_workspace)) < ndofs_global $nd",
+        ))
+    p2g = layout.packed_to_global
+    @inbounds for k in 1:no
+        v_owned[k] = y_workspace[p2g[k]]
+    end
+    return v_owned
+end
+
+"""
+    gather_ghosts_from_global_to_packed!(packed, x_global, layout) -> packed
+
+Fills only ghost slots `packed[layout.n_owned+1:layout.n_packed]` from
+`x_global` using [`packed_to_global`](@ref). The owned prefix is not modified.
+
+Allocation-free. Use after [`gather_owned_from_global_to_packed!`](@ref) when
+simulating MPI halos from a full global replica.
+"""
+function gather_ghosts_from_global_to_packed!(
+    packed::AbstractVector{Float64},
+    x_global::AbstractVector{Float64},
+    layout::PartitionPackedLayout,
+)
+    no = layout.n_owned
+    n = layout.n_packed
+    length(packed) ≥ n ||
+        throw(DimensionMismatch("packed length $(length(packed)) < n_packed $n"))
+    length(x_global) ≥ layout.ndofs_global ||
+        throw(DimensionMismatch("x_global length $(length(x_global)) < ndofs_global $(layout.ndofs_global)"))
+    p2g = layout.packed_to_global
+    @inbounds for k in (no + 1):n
+        packed[k] = x_global[p2g[k]]
+    end
+    return packed
+end
+
+"""
+    unpack_halo_recv_to_packed!(packed, recv_vals, exchange, layout) -> packed
+
+After MPI receives (or in serial tests), write neighbor halo values into
+`packed` ghost slots. `recv_vals[k]` aligns with `exchange.recv_dof[k]` global
+indices for neighbor `exchange.recv_neighbor[k]`.
+
+`exchange.part` must match `layout.part`. Each global DOF must appear in
+`layout.global_to_packed` with a positive index (ghost slot). Allocation-free.
+
+Pair [`build_rank_halo_exchanges`](@ref) with [`build_partition_packed_layout`](@ref)`(handler, …)`;
+pair [`build_matvec_halo_exchanges`](@ref) with [`build_partition_packed_layout_for_matvec`](@ref).
+"""
+function unpack_halo_recv_to_packed!(
+    packed::AbstractVector{Float64},
+    recv_vals::Vector{Vector{Float64}},
+    exchange::RankHaloExchange,
+    layout::PartitionPackedLayout,
+)
+    exchange.part == layout.part ||
+        throw(ArgumentError("exchange.part $(exchange.part) != layout.part $(layout.part)"))
+    length(recv_vals) == length(exchange.recv_dof) ==
+        length(exchange.recv_neighbor) ||
+        throw(DimensionMismatch("recv_vals / recv_dof / recv_neighbor length mismatch"))
+
+    @inbounds for k in eachindex(exchange.recv_dof)
+        rd = exchange.recv_dof[k]
+        rv = recv_vals[k]
+        length(rv) == length(rd) ||
+            throw(DimensionMismatch("recv_vals[$k] length $(length(rv)) != recv_dof[$k] $(length(rd))"))
+        for j in eachindex(rd)
+            g = rd[j]
+            (1 ≤ g ≤ layout.ndofs_global) ||
+                throw(ArgumentError("recv global dof index $g out of range"))
+            pk = layout.global_to_packed[g]
+            pk == 0 &&
+                throw(ArgumentError("recv global dof $g not in packed layout for part $(layout.part)"))
+            packed[pk] = rv[j]
+        end
+    end
+    return packed
+end
+
+"""
+    pack_halo_send_from_packed!(send_vals, packed, exchange, layout) -> send_vals
+
+Pack owned patch values into MPI send buffers. `send_vals[k][j]` receives
+`packed[layout.global_to_packed[g]]` for `g = exchange.send_dof[k][j]`.
+
+Allocation-free.
+"""
+function pack_halo_send_from_packed!(
+    send_vals::Vector{Vector{Float64}},
+    packed::AbstractVector{Float64},
+    exchange::RankHaloExchange,
+    layout::PartitionPackedLayout,
+)
+    exchange.part == layout.part ||
+        throw(ArgumentError("exchange.part $(exchange.part) != layout.part $(layout.part)"))
+    length(send_vals) == length(exchange.send_dof) ==
+        length(exchange.send_neighbor) ||
+        throw(DimensionMismatch("send_vals / send_dof / send_neighbor length mismatch"))
+
+    @inbounds for k in eachindex(exchange.send_dof)
+        sd = exchange.send_dof[k]
+        sv = send_vals[k]
+        length(sv) == length(sd) ||
+            throw(DimensionMismatch("send_vals[$k] length $(length(sv)) != send_dof[$k] $(length(sd))"))
+        for j in eachindex(sd)
+            g = sd[j]
+            (1 ≤ g ≤ layout.ndofs_global) ||
+                throw(ArgumentError("send global dof index $g out of range"))
+            pk = layout.global_to_packed[g]
+            pk == 0 &&
+                throw(ArgumentError("send global dof $g not in packed layout for part $(layout.part)"))
+            sv[j] = packed[pk]
+        end
+    end
+    return send_vals
+end
+
+"""
+    owned_dot_packed(u, v, layout) -> Float64
+
+Inner product over the **owned** prefix only:
+`sum_{k=1}^{n_owned} u[k] * v[k]`. For Krylov on domain-decomposed vectors stored
+in packed form, the global inner product is `MPI.Allreduce` of this local sum
+when each global DOF is owned by exactly one rank.
+
+Allocation-free.
+"""
+function owned_dot_packed(
+    u::AbstractVector{Float64},
+    v::AbstractVector{Float64},
+    layout::PartitionPackedLayout,
+)::Float64
+    no = layout.n_owned
+    length(u) ≥ no ||
+        throw(DimensionMismatch("u length $(length(u)) < n_owned $no"))
+    length(v) ≥ no ||
+        throw(DimensionMismatch("v length $(length(v)) < n_owned $no"))
+    s = 0.0
+    @inbounds for k in 1:no
+        s += u[k] * v[k]
+    end
+    return s
+end
+
+"""
+    owned_norm²_packed(u, layout) -> Float64
+
+[`owned_dot_packed`](@ref)`(u, u, layout)`.
+"""
+function owned_norm²_packed(u::AbstractVector{Float64}, layout::PartitionPackedLayout)::Float64
+    return owned_dot_packed(u, u, layout)
+end
+
+"""
+    owned_dot_global_vecs(a_global, b_global, layout) -> Float64
+
+`sum_{g : layout.owned_rows[g]} a_global[g] * b_global[g]`. Matches
+[`owned_dot_packed`](@ref) when `a_global` / `b_global` are full-length globals
+and `u`/`v` hold the owned entries in packed global-index order.
+
+Allocation-free.
+"""
+function owned_dot_global_vecs(
+    a_global::AbstractVector{Float64},
+    b_global::AbstractVector{Float64},
+    layout::PartitionPackedLayout,
+)::Float64
+    length(a_global) ≥ layout.ndofs_global ||
+        throw(DimensionMismatch("a_global length $(length(a_global)) < ndofs_global $(layout.ndofs_global)"))
+    length(b_global) ≥ layout.ndofs_global ||
+        throw(DimensionMismatch("b_global length $(length(b_global)) < ndofs_global $(layout.ndofs_global)"))
+    ow = layout.owned_rows
+    length(ow) == layout.ndofs_global ||
+        throw(DimensionMismatch("owned_rows length mismatch"))
+    s = 0.0
+    @inbounds for g in 1:layout.ndofs_global
+        ow[g] || continue
+        s += a_global[g] * b_global[g]
+    end
+    return s
+end