diff --git a/src/dofs/dof_connectivity.jl b/src/dofs/dof_connectivity.jl
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+# This file is a part of JuliaFEM.
+# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
+
+"""
+DOF connectivity structures for DOF-based assembly.
+
+Provides inverse mapping: DOF → Elements (which elements touch each DOF).
+
+**GPU-Compatible**: Uses bits types and fixed-size arrays for device transfer.
+**Zero-Allocation**: After initialization, all operations are allocation-free.
+"""
+
+# Import element and DOF manager interfaces (defined in elements.jl and dof_manager.jl)
+using ..JuliaFEM: element_dofs, DOFManager
+
+# ============================================================================
+# DOF-ELEMENT CONNECTION (GPU-Compatible Bits Type)
+# ============================================================================
+
+"""
+    DOFElementConnection
+
+Maps a global DOF to an element and local DOF index.
+
+**GPU-Compatible**: Bits type, can be transferred to GPU arrays.
+**Zero-Allocation**: Immutable struct, stack-allocated.
+
+# Fields
+- `elem_id::Int32`: Element ID (index in elements array)
+- `local_dof_idx::Int16`: Local DOF index within element (1-based)
+
+# Memory
+- 6 bytes per connection (Int32 + Int16)
+- Aligned to 8 bytes (padding)
+"""
+struct DOFElementConnection
+    elem_id::Int32      # Element ID (max 2^31 elements)
+    local_dof_idx::Int16  # Local DOF index (max 2^15 = 32k DOFs per element)
+    
+    function DOFElementConnection(elem_id::Integer, local_dof_idx::Integer)
+        # Validate ranges
+        if elem_id < 1 || elem_id > typemax(Int32)
+            error("Element ID $elem_id out of range [1, $(typemax(Int32))]")
+        end
+        if local_dof_idx < 1 || local_dof_idx > typemax(Int16)
+            error("Local DOF index $local_dof_idx out of range [1, $(typemax(Int16))]")
+        end
+        return new(Int32(elem_id), Int16(local_dof_idx))
+    end
+end
+
+# Convenience constructors
+DOFElementConnection(elem_id::Int32, local_dof_idx::Int16) = 
+    DOFElementConnection(Int(elem_id), Int(local_dof_idx))
+
+# Accessors
+elem_id(conn::DOFElementConnection) = Int(conn.elem_id)
+local_dof_idx(conn::DOFElementConnection) = Int(conn.local_dof_idx)
+
+# ============================================================================
+# DOF CONNECTIVITY (CPU Version - Variable-Length Vectors)
+# ============================================================================
+
+"""
+    DOFConnectivity
+
+Inverse mapping: For each global DOF, which elements contain it?
+
+**CPU Version**: Uses `Vector{Vector{DOFElementConnection}}` for variable-length lists.
+
+**Zero-Allocation After Init**: All arrays pre-allocated, no heap allocations during access.
+
+# Fields
+- `dof_to_elements::Vector{Vector{DOFElementConnection}}`: For each DOF, list of connections
+- `n_total_dofs::Int`: Total number of DOFs in system
+- `max_connections::Int`: Maximum number of elements touching any single DOF
+
+# Memory
+- ~16 bytes per connection (DOFElementConnection + Vector overhead)
+- O(n_elements × avg_dofs_per_element) total memory
+
+# Usage
+```julia
+connectivity = build_dof_connectivity(elements, dof_manager)
+
+# Access elements touching DOF i (zero-allocation!)
+connections = connectivity.dof_to_elements[dof_i]
+for conn in connections
+    elem = elements[conn.elem_id]
+    local_dof = conn.local_dof_idx
+    # Process...
+end
+```
+"""
+struct DOFConnectivity
+    dof_to_elements::Vector{Vector{DOFElementConnection}}
+    n_total_dofs::Int
+    max_connections::Int
+    
+    function DOFConnectivity(
+        dof_to_elements::Vector{Vector{DOFElementConnection}},
+        n_total_dofs::Int
+    )
+        # Compute max connections
+        max_conn = isempty(dof_to_elements) ? 0 : maximum(length, dof_to_elements)
+        return new(dof_to_elements, n_total_dofs, max_conn)
+    end
+end
+
+# Accessors
+Base.length(conn::DOFConnectivity) = conn.n_total_dofs
+Base.getindex(conn::DOFConnectivity, dof_i::Int) = conn.dof_to_elements[dof_i]
+
+"""
+    build_dof_connectivity(
+        elements::Vector{<:AbstractElement},
+        dof_manager::DOFManager
+    ) -> DOFConnectivity
+
+Build DOF-to-element connectivity from elements.
+
+**Complexity**: O(n_elements × avg_dofs_per_element) - optimal single pass.
+
+**Zero-Allocation After Init**: All arrays pre-allocated during build, no allocations during access.
+
+# Algorithm
+
+1. Initialize: `dof_to_elements = [DOFElementConnection[] for _ in 1:n_total_dofs]`
+2. Loop over elements:
+   - Get element's global DOF indices: `elem.dof_indices`
+   - For each (local_idx, global_dof):
+     - Push `DOFElementConnection(elem_id, local_idx)` to `dof_to_elements[global_dof]`
+3. Return `DOFConnectivity(dof_to_elements, n_total_dofs)`
+
+# Arguments
+- `elements`: Vector of elements with assigned DOF indices
+- `dof_manager`: DOF manager (for total DOF count)
+
+# Returns
+- `DOFConnectivity` with inverse mapping
+
+# Example
+
+```julia
+# Create elements with DOF assignment
+S = @DOFSet{u::DOF{Displacement{3}, Vertex}}
+ElemType = Element{Tetrahedron{4}, Lagrange{1}, S}
+elements, dof_mgr = create_elements!(mesh, ElemType)
+
+# Build connectivity (one-time cost)
+connectivity = build_dof_connectivity(elements, dof_mgr)
+
+# Use in DOF-based assembly (zero-allocation access!)
+for dof_i in 1:connectivity.n_total_dofs
+    connections = connectivity.dof_to_elements[dof_i]  # O(1) access
+    for conn in connections  # Zero-allocation iteration
+        elem = elements[conn.elem_id]
+        local_dof = conn.local_dof_idx
+        # Process...
+    end
+end
+```
+"""
+function build_dof_connectivity(
+    elements::Vector,
+    dof_manager::DOFManager
+)
+    n_total_dofs = dof_manager.total_dofs
+    
+    if n_total_dofs == 0
+        return DOFConnectivity(Vector{DOFElementConnection}[], 0)
+    end
+    
+    # Initialize: one vector per DOF
+    dof_to_elements = [DOFElementConnection[] for _ in 1:n_total_dofs]
+    
+    # Pre-allocate capacity estimate (reduce reallocations)
+    # Average: each DOF touched by ~6 elements (typical for 3D meshes)
+    avg_connections = 6
+    for vec in dof_to_elements
+        sizehint!(vec, avg_connections)
+    end
+    
+    # Loop over elements
+    for (elem_id, elem) in enumerate(elements)
+        # Get all global DOF indices for this element
+        dofs = element_dofs(elem)  # Returns NTuple{N, UInt64}
+        
+        # Register element with each DOF
+        for (local_idx, global_dof) in enumerate(dofs)
+            # Validate DOF index
+            if global_dof < 1 || global_dof > n_total_dofs
+                error("Invalid global DOF index $global_dof (must be in [1, $n_total_dofs])")
+            end
+            
+            # Create connection and push
+            conn = DOFElementConnection(elem_id, local_idx)
+            push!(dof_to_elements[global_dof], conn)
+        end
+    end
+    
+    return DOFConnectivity(dof_to_elements, n_total_dofs)
+end
+
+"""
+    build_dof_connectivity(
+        elements::Vector{<:AbstractElement},
+        n_total_dofs::Int
+    ) -> DOFConnectivity
+
+Build DOF connectivity without DOFManager (direct DOF count).
+
+Useful when DOF count is known but DOFManager is not available.
+"""
+function build_dof_connectivity(
+    elements::Vector,
+    n_total_dofs::Int
+)
+    if n_total_dofs == 0
+        return DOFConnectivity(Vector{DOFElementConnection}[], 0)
+    end
+    
+    # Initialize
+    dof_to_elements = [DOFElementConnection[] for _ in 1:n_total_dofs]
+    
+    # Pre-allocate capacity
+    avg_connections = 6
+    for vec in dof_to_elements
+        sizehint!(vec, avg_connections)
+    end
+    
+    # Build connectivity
+    for (elem_id, elem) in enumerate(elements)
+        dofs = element_dofs(elem)
+        for (local_idx, global_dof) in enumerate(dofs)
+            if global_dof < 1 || global_dof > n_total_dofs
+                error("Invalid global DOF index $global_dof (must be in [1, $n_total_dofs])")
+            end
+            conn = DOFElementConnection(elem_id, local_idx)
+            push!(dof_to_elements[global_dof], conn)
+        end
+    end
+    
+    return DOFConnectivity(dof_to_elements, n_total_dofs)
+end
+
+# ============================================================================
+# GPU-COMPATIBLE VERSION (Fixed-Size Arrays)
+# ============================================================================
+
+"""
+    DOFConnectivityGPU
+
+GPU-compatible DOF connectivity using fixed-size arrays.
+
+**GPU Transfer**: All arrays are `CuArray`-compatible (bits types only).
+
+**Memory**: Fixed-size matrices for predictable GPU memory usage.
+
+# Fields
+- `elem_ids::Matrix{Int32}`: Element IDs [max_connections, n_dofs]
+- `local_indices::Matrix{Int16}`: Local DOF indices [max_connections, n_dofs]
+- `counts::Vector{Int32}`: Actual connection count per DOF [n_dofs]
+- `n_total_dofs::Int`: Total DOFs
+- `max_connections::Int`: Maximum connections per DOF
+
+# Memory
+- ~(8 + 2) × max_connections × n_dofs bytes
+- More memory than CPU version, but GPU-friendly
+
+# Usage
+```julia
+# Build on CPU
+conn_gpu = build_dof_connectivity_gpu(elements, dof_manager, max_conn=20)
+
+# Transfer to GPU
+using CUDA
+elem_ids_gpu = CuArray(conn_gpu.elem_ids)
+local_indices_gpu = CuArray(conn_gpu.local_indices)
+counts_gpu = CuArray(conn_gpu.counts)
+
+# Use in GPU kernel
+@cuda threads=256 blocks=... dof_assembly_kernel!(
+    elem_ids_gpu, local_indices_gpu, counts_gpu, ...
+)
+```
+"""
+struct DOFConnectivityGPU
+    elem_ids::Matrix{Int32}        # [max_connections, n_dofs]
+    local_indices::Matrix{Int16}   # [max_connections, n_dofs]
+    counts::Vector{Int32}          # [n_dofs] - actual count per DOF
+    n_total_dofs::Int
+    max_connections::Int
+    
+    function DOFConnectivityGPU(
+        elem_ids::Matrix{Int32},
+        local_indices::Matrix{Int16},
+        counts::Vector{Int32},
+        n_total_dofs::Int,
+        max_connections::Int
+    )
+        # Validate dimensions
+        if size(elem_ids) != (max_connections, n_total_dofs)
+            error("elem_ids must be [$max_connections, $n_total_dofs]")
+        end
+        if size(local_indices) != (max_connections, n_total_dofs)
+            error("local_indices must be [$max_connections, $n_total_dofs]")
+        end
+        if length(counts) != n_total_dofs
+            error("counts must have length $n_total_dofs")
+        end
+        return new(elem_ids, local_indices, counts, n_total_dofs, max_connections)
+    end
+end
+
+"""
+    build_dof_connectivity_gpu(
+        elements::Vector{<:AbstractElement},
+        dof_manager::DOFManager;
+        max_connections::Int = 20
+    ) -> DOFConnectivityGPU
+
+Build GPU-compatible DOF connectivity with fixed-size arrays.
+
+# Arguments
+- `elements`: Vector of elements
+- `dof_manager`: DOF manager
+- `max_connections`: Maximum elements per DOF (default: 20)
+
+# Returns
+- `DOFConnectivityGPU` with fixed-size matrices
+
+# Notes
+- If a DOF has more than `max_connections` elements, an error is thrown.
+- Choose `max_connections` based on mesh connectivity (typically 6-12 for 3D).
+"""
+function build_dof_connectivity_gpu(
+    elements::Vector,
+    dof_manager::DOFManager;
+    max_connections::Int = 20
+)
+    n_total_dofs = dof_manager.total_dofs
+    
+    if n_total_dofs == 0
+        return DOFConnectivityGPU(
+            Matrix{Int32}(undef, 0, 0),
+            Matrix{Int16}(undef, 0, 0),
+            Int32[],
+            0,
+            0
+        )
+    end
+    
+    # Allocate fixed-size matrices
+    elem_ids = zeros(Int32, max_connections, n_total_dofs)
+    local_indices = zeros(Int16, max_connections, n_total_dofs)
+    counts = zeros(Int32, n_total_dofs)
+    
+    # Build connectivity
+    for (elem_id, elem) in enumerate(elements)
+        dofs = element_dofs(elem)
+        for (local_idx, global_dof) in enumerate(dofs)
+            if global_dof < 1 || global_dof > n_total_dofs
+                error("Invalid global DOF index $global_dof")
+            end
+            
+            count = counts[global_dof] + 1
+            if count > max_connections
+                error("DOF $global_dof has more than $max_connections connections " *
+                      "(found at least $count). Increase max_connections.")
+            end
+            
+            elem_ids[count, global_dof] = Int32(elem_id)
+            local_indices[count, global_dof] = Int16(local_idx)
+            counts[global_dof] = count
+        end
+    end
+    
+    return DOFConnectivityGPU(elem_ids, local_indices, counts, n_total_dofs, max_connections)
+end
+
+# ============================================================================
+# UTILITY FUNCTIONS
+# ============================================================================
+
+"""
+    connection_count(connectivity::DOFConnectivity, dof_i::Int) -> Int
+
+Get number of elements touching DOF i.
+
+**Zero-allocation**: Direct array length access.
+"""
+@inline connection_count(connectivity::DOFConnectivity, dof_i::Int) = 
+    length(connectivity.dof_to_elements[dof_i])
+
+"""
+    connection_count(connectivity::DOFConnectivityGPU, dof_i::Int) -> Int
+
+Get number of elements touching DOF i (GPU version).
+
+**Zero-allocation**: Direct array access.
+"""
+@inline connection_count(connectivity::DOFConnectivityGPU, dof_i::Int) = 
+    Int(connectivity.counts[dof_i])
+
+"""
+    is_empty(connectivity::DOFConnectivity, dof_i::Int) -> Bool
+
+Check if DOF i has no connections.
+
+**Zero-allocation**: Direct array length check.
+"""
+@inline is_empty(connectivity::DOFConnectivity, dof_i::Int) = 
+    isempty(connectivity.dof_to_elements[dof_i])
+
+"""
+    is_empty(connectivity::DOFConnectivityGPU, dof_i::Int) -> Bool
+
+Check if DOF i has no connections (GPU version).
+
+**Zero-allocation**: Direct array access.
+"""
+@inline is_empty(connectivity::DOFConnectivityGPU, dof_i::Int) = 
+    connectivity.counts[dof_i] == 0
+
+# ============================================================================
+# EXPORTS
+# ============================================================================
+
+# Export types and functions
+export DOFElementConnection, DOFConnectivity, DOFConnectivityGPU
+export build_dof_connectivity, build_dof_connectivity_gpu
+export connection_count, is_empty
+export elem_id, local_dof_idx