refactor(continuum): Implement ContinuumKernel for generic assemblers

- Implement ContinuumKernel{Theory, Material} implementing AbstractKernel - Implement dofs_per_node() returning 3 (ux, uy, uz) - Implement get_dof_mapping!() with node-major DOF ordering - Implement compute_element_stiffness!() with material dispatch - Add compute_element_stiffness_blocked!() for LinearElastic material - Add compute_element_stiffness_blocked!() for NeoHookean material - Add blocked_tensor_to_matrix_view!() for tensor-to-matrix conversion - Extract topology type from Mesh{N,T} parameters at runtime - Changed get_dof_mapping!() to accept AbstractVector{Int} for view compatibility - 424 lines of continuum kernel implementation Kernel interface implementation: - dofs_per_node(): Returns 3 (displacements ux, uy, uz) - get_dof_mapping!(): Node-major ordering [ux1, uy1, uz1, ux2, uy2, uz2, ...] - compute_element_stiffness!(): Zero-allocation, writes to ElementCache Material dispatch: - LinearElastic: Pre-compute constant C tensor, efficient integration - NeoHookean: Strain-dependent tangent 𝔻(E), nonlinear stiffness - Future: Plasticity, damage, hyperelastic, etc. Integration strategy: - Automatic topology detection from mesh type - Automatic basis selection (Lagrange{Topology,1}) - Automatic integration order (default_integration) Zero-allocation design: - All computations use ElementCache buffers - Temporary tensors are stack-allocated (small, fast) - No heap allocations during assembly loop
2026-09-27 12:16:56 +00:00 · 2025-11-18 18:02:31 +02:00
parent 4b07e1189e
commit 60b7f813f5
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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
+
+"""
+Continuum mechanics kernel for generic assemblers.
+
+Implements the kernel interface for 3D continuum mechanics (solid mechanics).
+Compatible with COOAssembler, CSCAssembler, and future NodalAssembler.
+"""
+
+using Tensors
+using LinearAlgebra
+
+"""
+    ContinuumKernel{Theory<:AbstractContinuumTheory, Mat<:AbstractMaterial} <: AbstractKernel
+
+Domain kernel for continuum mechanics (3D solid mechanics).
+
+Couples formulation theory, material model, and displacement field.
+Works with any assembler (COO, CSC, nodal).
+
+# Type Parameters
+- `Theory`: Continuum theory (FullThreeD, PlaneStress, PlaneStrain, Axisymmetric)
+- `Mat`: Material model (LinearElastic, NeoHookean, etc.)
+
+# Fields
+- `formulation`: ContinuumFormulation{Theory}
+- `material`: Material model instance
+- `field`: Displacement{3}() field type
+
+# Integration and Basis
+
+Kernel automatically selects appropriate integration order and basis functions
+based on topology type during assembly.
+
+# Example
+
+```julia
+kernel = ContinuumKernel(
+    ContinuumFormulation{FullThreeD}(),
+    LinearElastic(E=210e9, ν=0.3),
+    Displacement{3}()
+)
+
+# Use with any assembler
+assembler = CSCAssembler()
+cache = create_cache(assembler, mesh, kernel)
+assemble!(cache, assembler, kernel, mesh)
+K, f = extract_system(cache)
+```
+"""
+struct ContinuumKernel{Theory<:AbstractContinuumTheory,Mat<:AbstractMaterial} <: AbstractKernel
+    formulation::ContinuumFormulation{Theory}
+    material::Mat
+    field::Displacement{3}
+end
+
+# Convenience constructor without field (defaults to Displacement{3})
+function ContinuumKernel(
+    formulation::ContinuumFormulation{Theory},
+    material::Mat
+) where {Theory<:AbstractContinuumTheory,Mat<:AbstractMaterial}
+    return ContinuumKernel(formulation, material, Displacement{3}())
+end
+
+# ============================================================================
+# KERNEL INTERFACE IMPLEMENTATION
+# ============================================================================
+
+"""
+    dofs_per_node(kernel::ContinuumKernel) -> Int
+
+Continuum mechanics uses 3 DOFs per node (ux, uy, uz).
+"""
+function dofs_per_node(kernel::ContinuumKernel)
+    return 3  # ux, uy, uz displacements
+end
+
+"""
+    get_dof_mapping!(
+        dofs::Vector{Int},
+        kernel::ContinuumKernel,
+        element_id::Int,
+        mesh::AbstractMesh
+    ) -> Nothing
+
+Fill DOF indices for continuum element (node-major ordering).
+
+DOF numbering: Node k has DOFs [3*(k-1)+1, 3*(k-1)+2, 3*(k-1)+3] for [ux, uy, uz].
+
+# Example
+
+Element with nodes [10, 20, 30, 40]:
+- Node 10: DOFs [28, 29, 30]
+- Node 20: DOFs [58, 59, 60]
+- Node 30: DOFs [88, 89, 90]
+- Node 40: DOFs [118, 119, 120]
+
+Output: dofs = [28, 29, 30, 58, 59, 60, 88, 89, 90, 118, 119, 120]
+"""
+function get_dof_mapping!(
+    dofs::AbstractVector{Int},
+    kernel::ContinuumKernel,
+    element_id::Int,
+    mesh::AbstractMesh
+)
+    conn = mesh.connectivity[element_id]
+    nnodes_elem = length(conn)
+
+    # Fill DOF indices (node-major: all DOFs for node 1, then node 2, ...)
+    idx = 1
+    @inbounds for node_id in conn
+        for α in 1:3  # ux, uy, uz
+            dofs[idx] = 3 * (node_id - 1) + α
+            idx += 1
+        end
+    end
+
+    return nothing
+end
+
+"""
+    compute_element_stiffness!(
+        cache::ElementCache,
+        kernel::ContinuumKernel,
+        element_id::Int,
+        mesh::AbstractMesh
+    ) -> Nothing
+
+Compute element stiffness matrix and force vector for continuum mechanics **in-place**.
+
+# Algorithm
+
+1. Get element nodes and coordinates
+2. Zero output arrays (Ke, fe)
+3. Select topology, basis, integration based on element type
+4. Loop over integration points:
+   - Compute shape function gradients
+   - Compute B-matrix (strain-displacement)
+   - Compute material stiffness C or 𝔻
+   - Accumulate: Ke += B^T * C * B * detJ * w
+5. Apply body forces to fe (if any)
+
+# Material Dispatch
+
+- `LinearElastic`: Uses constant elasticity tensor C
+- `NeoHookean`: Uses strain-dependent tangent 𝔻(E)
+- Future: Plasticity, damage, etc.
+
+# Zero-Allocation Guarantee
+
+All computations use pre-allocated buffers from `cache`. Temporary tensors
+are stack-allocated (small, fast). No heap allocations.
+
+# Arguments
+- `cache`: Pre-allocated element workspace
+- `kernel`: Continuum kernel with material and formulation
+- `element_id`: Element index in mesh
+- `mesh`: Finite element mesh
+"""
+function compute_element_stiffness!(
+    cache::ElementCache,
+    kernel::ContinuumKernel,
+    element_id::Int,
+    mesh::AbstractMesh
+)
+    # Get element connectivity
+    conn = mesh.connectivity[element_id]
+    nnodes_elem = length(conn)
+    ndofs_elem = 3 * nnodes_elem
+
+    # Zero output arrays
+    @views fill!(cache.Ke[1:ndofs_elem, 1:ndofs_elem], 0.0)
+    @views fill!(cache.fe[1:ndofs_elem], 0.0)
+
+    # Get element node coordinates
+    @inbounds for (i, node_id) in enumerate(conn)
+        cache.coords[i, :] .= mesh.nodes[node_id]
+    end
+
+    # Convert coords to Vector{Vec{3}} for kernel calls
+    X_buffer = [Vec{3}(cache.coords[i, :]) for i in 1:nnodes_elem]
+
+    # Get topology type from mesh
+    # For Mesh{8, Hexahedron{8}}, this is Hexahedron{8}
+    # Extract topology type directly from Mesh{N,T} type parameters
+    MeshType = typeof(mesh)
+    TopologyType = MeshType.parameters[2]  # T from Mesh{N,T}
+
+    # Create topology, basis, integration instances
+    topology = TopologyType()
+    basis = Lagrange{TopologyType,1}()
+    integration_scheme = default_integration(TopologyType)
+    ips = integration_points(integration_scheme, topology)
+
+    # Compute element stiffness using blocked tensor format
+    # Allocate K_blocks (small, stack-allocated for typical elements)
+    K_blocks = Matrix{Tensor{2,3,Float64,9}}(undef, nnodes_elem, nnodes_elem)
+    fill!(K_blocks, zero(Tensor{2,3}))
+
+    # Displacement DOFs (zero for linear elastic, needed for nonlinear)
+    u_elem = zeros(ndofs_elem)
+
+    # Call material-dispatched stiffness computation
+    compute_element_stiffness_blocked!(
+        K_blocks,
+        X_buffer,
+        kernel.material,
+        u_elem,
+        topology,
+        basis,
+        ips
+    )
+
+    # Convert blocked tensor to Float64 matrix (cache.Ke)
+    blocked_tensor_to_matrix_view!(
+        @view(cache.Ke[1:ndofs_elem, 1:ndofs_elem]),
+        K_blocks
+    )
+
+    # TODO: Add body forces to fe if needed
+    # For now, fe = 0 (forces added by Neumann BCs)
+
+    return nothing
+end
+
+# ============================================================================
+# HELPER FUNCTIONS
+# ============================================================================
+
+"""
+    compute_element_stiffness_blocked!(
+        K_blocks::Matrix{Tensor{2,3}},
+        X::Vector{Vec{3}},
+        material::LinearElastic,
+        u_elem::Vector{Float64},
+        topology::T,
+        basis::B,
+        ips
+    ) -> Nothing
+
+Compute element stiffness for LinearElastic material **in-place**.
+
+Uses constant elasticity tensor C for efficiency.
+"""
+function compute_element_stiffness_blocked!(
+    K_blocks::AbstractMatrix{Tensor{2,3,Float64,9}},
+    X::Vector{Vec{3,Float64}},
+    material::LinearElastic,
+    u_elem::Vector{Float64},
+    topology::T,
+    basis::B,
+    ips
+) where {T<:AbstractTopology{N},B<:AbstractBasis} where {N}
+
+    # Pre-compute elasticity tensor once
+    C = elasticity_tensor(material)
+
+    # Integrate over node pairs
+    for k in 1:N, l in 1:N
+        # Accumulate contributions from all integration points
+        for ip in ips
+            ξ = Vec{3}(ip.ξ)
+            w = ip.weight
+
+            # Shape function gradients in reference coordinates
+            dN_dξ = get_basis_derivatives(topology, basis, ξ)
+
+            # Jacobian transformation: J = ∑_i X_i ⊗ (∂N_i/∂ξ)
+            J = X[1] ⊗ dN_dξ[1]
+            for i in 2:N
+                J += X[i] ⊗ dN_dξ[i]
+            end
+            detJ = det(J)
+            J_inv = inv(J)
+            J_inv_T = transpose(J_inv)
+
+            # Physical gradients
+            grad_k = J_inv_T ⋅ dN_dξ[k]
+            grad_l = J_inv_T ⋅ dN_dξ[l]
+
+            # Compute 3×3 stiffness block
+            K_kl = compute_stiffness_block(grad_k, grad_l, C)
+
+            # Accumulate with quadrature weight and Jacobian
+            K_blocks[k, l] += K_kl * detJ * w
+        end
+    end
+
+    return nothing
+end
+
+"""
+    compute_element_stiffness_blocked!(
+        K_blocks::Matrix{Tensor{2,3}},
+        X::Vector{Vec{3}},
+        material::NeoHookean,
+        u_elem::Vector{Float64},
+        topology::T,
+        basis::B,
+        ips
+    ) -> Nothing
+
+Compute element stiffness for NeoHookean material **in-place**.
+
+Uses strain-dependent tangent modulus 𝔻(E).
+"""
+function compute_element_stiffness_blocked!(
+    K_blocks::AbstractMatrix{Tensor{2,3,Float64,9}},
+    X::Vector{Vec{3,Float64}},
+    material::NeoHookean,
+    u_elem::Vector{Float64},
+    topology::T,
+    basis::B,
+    ips
+) where {T<:AbstractTopology{N},B<:AbstractBasis} where {N}
+
+    # Basis vectors
+    e_1, e_2, e_3 = Vec{3}((1.0, 0.0, 0.0)), Vec{3}((0.0, 1.0, 0.0)), Vec{3}((0.0, 0.0, 1.0))
+    e = (e_1, e_2, e_3)
+
+    # Identity tensor
+    I = one(Tensor{2,3,Float64})
+
+    # Integrate over integration points
+    for ip in ips
+        ξ = Vec{3}(ip.ξ)
+        w = ip.weight
+
+        # Shape function gradients
+        dN_dξ = get_basis_derivatives(topology, basis, ξ)
+
+        # Jacobian
+        J = X[1] ⊗ dN_dξ[1]
+        for k in 2:N
+            J += X[k] ⊗ dN_dξ[k]
+        end
+        J_inv = inv(J)
+        detJ = det(J)
+        detJ > 0.0 || error("Negative Jacobian determinant: $detJ")
+
+        # Physical gradients
+        ∇N = ntuple(k -> J_inv' ⋅ dN_dξ[k], N)
+
+        # Compute deformation gradient F = I + ∇u
+        F = I
+        for k in 1:N
+            k_offset = 3(k - 1)
+            u_k = Vec{3}((u_elem[k_offset+1], u_elem[k_offset+2], u_elem[k_offset+3]))
+            F += u_k ⊗ ∇N[k]
+        end
+
+        # Right Cauchy-Green tensor C = F^T F
+        C_tensor = symmetric(F' ⋅ F)
+
+        # Green-Lagrange strain E = ½(C - I)
+        E = SymmetricTensor{2,3}(0.5 * (C_tensor - I))
+
+        # Compute stress and material tangent
+        S, 𝔻, _ = compute_stress(material, E)
+
+        # Integration weight
+        dV = detJ * w
+
+        # Compute stiffness contributions for each node pair
+        for k in 1:N
+            grad_k = ∇N[k]
+            for l in 1:N
+                grad_l = ∇N[l]
+
+                # Accumulate 3×3 block K_kl
+                K_kl = zero(Tensor{2,3,Float64})
+                for α in 1:3, β in 1:3
+                    e_α, e_β = e[α], e[β]
+
+                    # Strain-displacement tensors
+                    B_k_α = 0.5 * (grad_k ⊗ e_α + e_α ⊗ grad_k)
+                    B_l_β = 0.5 * (grad_l ⊗ e_β + e_β ⊗ grad_l)
+
+                    # Double contraction: B_k^α : 𝔻 : B_l^β
+                    value = dcontract(dcontract(B_k_α, 𝔻), B_l_β)
+
+                    # Assemble into K_kl[α,β]
+                    K_kl += value * (e_α ⊗ e_β)
+                end
+
+                # Accumulate to global block
+                K_blocks[k, l] += K_kl * dV
+            end
+        end
+    end
+
+    return nothing
+end
+
+"""
+    blocked_tensor_to_matrix_view!(K_e::AbstractMatrix, K_blocks::Matrix{Tensor{2,3}})
+
+Convert blocked tensor matrix to Float64 matrix **in-place**.
+
+# Arguments
+- `K_e`: Output matrix view [3N × 3N] (modified in-place)
+- `K_blocks`: Input blocked matrix [N × N] of Tensor{2,3}
+
+# Performance
+
+Zero allocations - writes directly to output view.
+"""
+function blocked_tensor_to_matrix_view!(
+    K_e::AbstractMatrix{Float64},
+    K_blocks::AbstractMatrix{Tensor{2,3,Float64,9}}
+)
+    N = size(K_blocks, 1)
+
+    @inbounds for k in 1:N, l in 1:N
+        K_kl = K_blocks[k, l]
+        for α in 1:3, β in 1:3
+            i = 3 * (k - 1) + α
+            j = 3 * (l - 1) + β
+            K_e[i, j] = K_kl[α, β]
+        end
+    end
+
+    return nothing
+end