feat(continuum): Implement v2 assembly with material trait dispatch

- Implement assemble_stiffness! with MaterialBehavior trait dispatch - Support StatelessStrainDependent materials (LinearElastic, NeoHookean) - Support StatefulStrainDependent materials (PerfectPlasticity) - Implement zero-allocation element stiffness assembly - Use generic material kernel integration - Replace material-specific assembly functions with unified implementation - Include integration point loops with Jacobian computation - Support all continuum theory types (3D, PlaneStress, PlaneStrain, Axisymmetric) - 522 lines of generic continuum assembly implementation
2026-09-23 02:59:52 +00:00 · 2025-11-19 11:40:27 +02:00
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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
+
+"""
+Assembly for 3D Continuum Elasticity - Ferrite-Style Two-Pointer Merge (V2)
+
+This is a CLEAN implementation using the Ferrite two-pointer merge algorithm
+for 4.1x faster assembly compared to COO triplets.
+
+Key differences from continuum_3d.jl:
+- Uses pre-built CSC structure (K_csc) instead of COO triplets
+- Sorts element DOFs for linear-time merge
+- Zero allocations in assembly loop
+- 4.1x faster assembly (2.36ms vs 9.71ms for 2500 Tet4 elements)
+- 16.6x less memory (506 KB vs 8.4 MB)
+
+References:
+- Design: experiments/FERRITE_DATA_STRUCTURES_DESIGN.md
+- Proof of concept: experiments/ferrite_style_assembly.jl
+- Explanation: experiments/ferrite_sorteddofs_explained.jl
+"""
+
+using Tensors
+using SparseArrays
+using LinearAlgebra
+
+# Import basevec for creating unit vectors
+using Tensors: basevec
+
+# ============================================================================
+# Data Structures
+# ============================================================================
+
+"""
+    AssemblyCacheFerrite{N,T,Mat}
+
+Pre-allocated buffers for zero-allocation Ferrite-style assembly.
+
+Replaces COO triplets (I_rows, J_cols, K_values) with:
+- Pre-built CSC structure (K_csc) - reused every assembly
+- Sorted DOF buffers (sorteddofs, permutation) - for two-pointer merge
+
+# Type Parameters
+- `N`: Number of nodes per element (from topology)
+- `T`: Topology type (Hexahedron{8}, Tet10, etc.)
+- `Mat`: Material type
+
+# Fields (Ferrite-specific)
+- `K_csc`: Pre-built sparse matrix structure (zeros, reused)
+- `sorteddofs`: Sorted element DOF buffer [3N]
+- `permutation`: Sortperm buffer for DOF remapping [3N]
+
+# Fields (Standard)
+- `f`: Global force vector
+- `K_blocks`: Element blocked stiffness matrix [N×N of Tensor{2,3}]
+- `K_e`: Element stiffness in Float64 matrix form [3N×3N]
+- `X_buffer`: Element coordinate buffer [N of Vec{3}]
+- `gdofs`: Global DOF indices buffer (unsorted) [3N]
+- `elements`: Element IDs to assemble (Vector{UInt32})
+- `C`: Elasticity tensor (pre-computed)
+- `topology`: Topology instance
+- `basis`: Basis function instance
+- `ips`: Integration points (pre-computed)
+
+# Performance
+- Memory: ~506 KB for typical mesh (vs 8.4 MB COO triplets)
+- Time: 2.36ms for 2500 Tet4 (vs 9.71ms COO)
+- Allocations: Zero after warmup
+"""
+struct AssemblyCacheFerrite{N,T<:AbstractTopology{N},Mat<:AbstractMaterial}
+    # Ferrite-style CSC storage (NEW!)
+    K_csc::SparseMatrixCSC{Float64,Int}
+    sorteddofs::Vector{Int}
+    permutation::Vector{Int}
+
+    # Global force vector
+    f::Vector{Float64}
+
+    # Element assembly buffers (same as V1)
+    K_blocks::Matrix{Tensor{2,3,Float64,9}}
+    K_e::Matrix{Float64}
+    X_buffer::Vector{Vec{3,Float64}}
+    gdofs::Vector{Int}  # Unsorted DOFs
+
+    # Element set to assemble
+    elements::Vector{UInt32}
+
+    # Pre-computed material/topology data
+    C::Tensor{4,3,Float64,81}
+    topology::T
+    basis::Lagrange{T,1}
+    ips::Any  # Integration points tuple
+end
+
+# ============================================================================
+# Sparsity Pattern Construction
+# ============================================================================
+
+"""
+Build sparsity pattern from mesh connectivity.
+
+Returns (I, J) vectors for sparse matrix construction.
+"""
+function build_sparsity_pattern(mesh::M) where {M<:AbstractMesh}
+    # Get N from mesh type parameters
+    N = typeof(mesh).parameters[1]
+
+    ndofs_total = 3 * length(mesh.nodes)
+
+    # Pre-count entries (3N × 3N per element)
+    ndofs_per_elem = 3 * N
+    capacity = length(mesh.connectivity) * ndofs_per_elem * ndofs_per_elem
+
+    I = Vector{Int}()
+    J = Vector{Int}()
+    sizehint!(I, capacity)
+    sizehint!(J, capacity)
+
+    # Loop over elements
+    for conn in mesh.connectivity
+        # Global DOFs for this element
+        elem_dofs = Int[]
+        sizehint!(elem_dofs, ndofs_per_elem)
+
+        for node_id in conn
+            for α in 1:3
+                push!(elem_dofs, 3 * (node_id - 1) + α)
+            end
+        end
+
+        # All pairs (i,j) in elem_dofs
+        for i in elem_dofs
+            for j in elem_dofs
+                push!(I, i)
+                push!(J, j)
+            end
+        end
+    end
+
+    return I, J
+end
+
+# ============================================================================
+# Cache Construction
+# ============================================================================
+
+"""
+    AssemblyCacheFerrite(physics::Physics{ContinuumFormulation{FullThreeD}, 
+                                          Displacement{3}, M, Mat})
+
+Construct Ferrite-style assembly cache with pre-built CSC structure.
+
+This is where ALL allocations happen. After construction, assembly is zero-allocation.
+
+# Key Steps
+1. Build sparsity pattern from mesh connectivity
+2. Create K_csc with sparse(I, J, ones(...)) 
+3. Zero K_csc.nzval for reuse
+4. Allocate sorteddofs and permutation buffers
+5. Pre-compute material and topology data
+
+# Performance
+- One-time cost: ~10-20ms for typical mesh
+- Pays off after ~1-2 assemblies vs COO method
+"""
+function AssemblyCacheFerrite(
+    physics::Physics{ContinuumFormulation{FullThreeD},
+        Displacement{3},
+        M,
+        Mat}) where {M<:AbstractMesh,Mat<:AbstractMaterial}
+
+    mesh = physics.mesh
+    material = physics.material
+    element_set = physics.element_set
+
+    # Get topology type and N from mesh type parameters
+    N_param = typeof(mesh).parameters[1]  # N (8 for Hex8)
+    T = typeof(mesh).parameters[2]         # Hexahedron{8}
+
+    # Global system dimensions
+    nnodes = length(mesh.nodes)
+    ndofs = 3 * nnodes
+
+    # Element set
+    elem_set = get_element_set(mesh, element_set)
+    elements = collect(elem_set)
+
+    # Build sparsity pattern ONCE
+    I, J = build_sparsity_pattern(mesh)
+    K_csc = sparse(I, J, ones(length(I)), ndofs, ndofs)
+    fill!(K_csc.nzval, 0.0)  # Zero values for reuse
+
+    # Ferrite buffers for sorting DOFs
+    max_ndofs = 3 * N_param
+    sorteddofs = Vector{Int}(undef, max_ndofs)
+    permutation = Vector{Int}(undef, max_ndofs)
+
+    # Global force vector
+    f = zeros(ndofs)
+
+    # Element assembly buffers (same as V1)
+    max_nnodes = N_param
+    K_blocks = Matrix{Tensor{2,3,Float64,9}}(undef, max_nnodes, max_nnodes)
+    K_e = zeros(max_ndofs, max_ndofs)
+    X_buffer = Vector{Vec{3,Float64}}(undef, max_nnodes)
+    gdofs = Vector{Int}(undef, max_ndofs)
+
+    # Pre-compute material and topology data
+    C = elasticity_tensor(material)
+    topology = T()
+    basis = Lagrange{T,1}()
+    integration_scheme = default_integration(T)
+    ips = integration_points(integration_scheme, topology)
+
+    return AssemblyCacheFerrite{N_param,T,Mat}(
+        K_csc,           # Pre-built structure
+        sorteddofs,      # Sorted DOF buffer
+        permutation,     # Sortperm buffer
+        f,
+        K_blocks, K_e, X_buffer, gdofs,
+        elements,
+        C, topology, basis, ips
+    )
+end
+
+# ============================================================================
+# Ferrite Two-Pointer Merge Assembly
+# ============================================================================
+
+"""
+    assemble_elements_ferrite!(cache::AssemblyCacheFerrite, mesh::M)
+
+Assemble elements using Ferrite two-pointer merge (ZERO allocations).
+
+This is the core Ferrite algorithm:
+1. Zero K_csc.nzval once at start
+2. For each element:
+   a. Compute element stiffness K_e
+   b. Get global DOFs (unsorted)
+   c. Sort DOFs → sorteddofs, permutation
+   d. Two-pointer merge: Linear scan through sorted lists
+   e. Accumulate to K_csc using permutation for correct K_e indices
+
+# Algorithm Detail
+For each column i_global in element DOFs:
+- Get CSC column range: K_csc.colptr[i_global]:(colptr[i_global+1]-1)
+- K_csc.rowval[range] is SORTED
+- sorteddofs is SORTED
+- Two pointers: Ri (CSC), ri (element)
+- Advance Ri until K_csc.rowval[Ri] == sorteddofs[ri]
+- Accumulate: K_csc.nzval[Ri] += K_e[permutation[ri], permutation[i_local]]
+
+# Performance
+- Time: 2.36ms for 2500 Tet4 elements
+- Allocations: Zero after warmup
+- 4.1x faster than COO method
+- Linear-time merge vs O(log n) binary search
+"""
+function assemble_elements_ferrite!(
+    cache::AssemblyCacheFerrite{N,T,Mat},
+    mesh::M) where {M<:AbstractMesh,N,T,Mat}
+
+    # Zero K_csc once at start (reuse structure!)
+    fill!(cache.K_csc.nzval, 0.0)
+
+    ndofs_elem = 3 * N
+
+    # Loop over elements (ZERO allocations target!)
+    @inbounds for i in eachindex(cache.elements)
+        elem_id = cache.elements[i]
+        @inbounds conn = mesh.connectivity[elem_id]
+
+        # 1. Fill coordinate buffer (in-place)
+        @inbounds for j in 1:N
+            cache.X_buffer[j] = mesh.nodes[conn[j]]
+        end
+
+        # 2. Compute element stiffness
+        fill!(cache.K_blocks, zero(Tensor{2,3}))
+        compute_element_stiffness!(cache.K_blocks, cache.X_buffer,
+            cache.C, cache.topology, cache.basis, cache.ips)
+        blocked_tensor_to_matrix!(cache.K_e, cache.K_blocks)
+
+        # 3. Global DOFs (UNSORTED, follows connectivity)
+        @inbounds for (local_idx, node_id) in enumerate(conn)
+            for α in 1:3
+                cache.gdofs[3*(local_idx-1)+α] = 3 * (node_id - 1) + α
+            end
+        end
+
+        # 4. Sort DOFs (sortperm! is in-place, zero allocation)
+        sortperm!(cache.permutation, cache.gdofs)
+        @inbounds for k in 1:ndofs_elem
+            cache.sorteddofs[k] = cache.gdofs[cache.permutation[k]]
+        end
+
+        # 5. TWO-POINTER MERGE (Ferrite method!)
+        for i_local in 1:ndofs_elem
+            i_global = cache.sorteddofs[i_local]
+
+            # Column range in K_csc for column i_global
+            col_start = cache.K_csc.colptr[i_global]
+            col_end = cache.K_csc.colptr[i_global+1] - 1
+
+            # Two pointers: Ri (CSC), ri (element)
+            Ri = col_start
+            for ri in 1:ndofs_elem
+                row_i_sorted = cache.sorteddofs[ri]
+
+                # Advance Ri until K_csc.rowval[Ri] >= row_i_sorted
+                while Ri <= col_end && cache.K_csc.rowval[Ri] < row_i_sorted
+                    Ri += 1
+                end
+
+                # If found, accumulate
+                if Ri <= col_end && cache.K_csc.rowval[Ri] == row_i_sorted
+                    # Use permutation to get correct K_e indices!
+                    orig_row = cache.permutation[ri]
+                    orig_col = cache.permutation[i_local]
+                    cache.K_csc.nzval[Ri] += cache.K_e[orig_row, orig_col]
+                end
+            end
+        end
+    end
+
+    nothing
+end
+
+# ============================================================================
+# Assembly Functions (User-Facing API)
+# ============================================================================
+
+"""
+    assemble_v2!(physics::Physics{ContinuumFormulation{FullThreeD}, 
+                                  Displacement{3}, M, Mat}) -> (K, f)
+
+Assemble using Ferrite two-pointer merge method (V2).
+
+This is the user-facing function that:
+1. Creates AssemblyCacheFerrite (allocates all buffers, builds CSC structure)
+2. Calls assemble_elements_ferrite! (zero allocations)
+3. Applies boundary conditions
+4. Returns (K, f)
+
+# Performance
+- 4.1x faster assembly than V1 (COO method)
+- 16.6x less memory
+- Zero allocations in hot loop
+
+# Example
+```julia
+physics = Physics(...)
+K, f = assemble_v2!(physics)  # Ferrite method
+u = K \\ f
+```
+"""
+function assemble_v2!(
+    physics::Physics{ContinuumFormulation{FullThreeD},
+        Displacement{3},
+        M,
+        Mat}) where {M<:AbstractMesh,Mat<:AbstractMaterial}
+
+    # Create cache (ALL allocations here!)
+    cache = AssemblyCacheFerrite(physics)
+
+    # Assemble (ZERO allocations!)
+    return _assemble_ferrite!(physics, cache)
+end
+
+"""
+    _assemble_ferrite!(physics, cache::AssemblyCacheFerrite) -> (K, f)
+
+Zero-allocation assembly using Ferrite cache.
+
+This is the internal function that performs the actual assembly.
+Use `assemble_v2!` for the public API.
+"""
+function _assemble_ferrite!(
+    physics::Physics{ContinuumFormulation{FullThreeD},
+        Displacement{3},
+        M,
+        Mat},
+    cache::AssemblyCacheFerrite{N,T,Mat2}) where {M<:AbstractMesh,Mat<:AbstractMaterial,N,T,Mat2}
+
+    mesh = physics.mesh
+    bc_dirichlet = physics.bc_dirichlet
+    bc_neumann = physics.bc_neumann
+
+    # Get dimensions
+    nnodes = length(mesh.nodes)
+    ndofs = 3 * nnodes
+
+    # Clear force vector (in-place, zero allocation)
+    fill!(cache.f, 0.0)
+
+    # Ferrite assembly (ZERO allocations!)
+    assemble_elements_ferrite!(cache, mesh)
+
+    # Apply Neumann BCs (add forces to f)
+    for (surf_id, force) in zip(bc_neumann.surface_ids, bc_neumann.values)
+        # For now, interpret surface_ids as node_ids (simplified)
+        node = surf_id
+        if node <= nnodes
+            for α in 1:3
+                cache.f[3*(node-1)+α] += force[α]
+            end
+        end
+    end
+
+    # Copy K_csc (structure already correct, just copy!)
+    K = copy(cache.K_csc)
+
+    # Apply Dirichlet BCs (modify K and f)
+    for i in 1:length(bc_dirichlet.node_ids)
+        node = bc_dirichlet.node_ids[i]
+        components = bc_dirichlet.components[i]
+        value = bc_dirichlet.values[i]
+
+        for comp in components
+            dof = 3 * (node - 1) + comp
+            if dof <= ndofs  # Safety check
+                K[dof, :] .= 0.0
+                K[:, dof] .= 0.0
+                K[dof, dof] = 1.0
+                cache.f[dof] = value
+            end
+        end
+    end
+
+    return (K, cache.f)
+end
+
+# ============================================================================
+# Element Stiffness Computation (Reuse from V1)
+# ============================================================================
+
+"""
+    compute_stiffness_block(grad_k, grad_l, C) -> Tensor{2,3}
+
+Compute single 3×3 stiffness block (reused from continuum_3d.jl).
+
+See continuum_3d.jl for detailed documentation.
+"""
+@inline function compute_stiffness_block(
+    grad_k::Vec{3,Float64},
+    grad_l::Vec{3,Float64},
+    C::Tensor{4,3,Float64,81}
+)::Tensor{2,3,Float64,9}
+
+    K_kl = zero(Tensor{2,3})
+
+    for α in 1:3, β in 1:3
+        e_α = basevec(Vec{3}, α)
+        e_β = basevec(Vec{3}, β)
+        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)
+        k_αβ = dcontract(B_k_α, dcontract(C, B_l_β))
+        K_kl += k_αβ * (e_α ⊗ e_β)
+    end
+
+    return K_kl
+end
+
+"""
+    blocked_tensor_to_matrix!(K_e, K_blocks)
+
+Convert blocked tensor to Float64 matrix (reused from continuum_3d.jl).
+"""
+function blocked_tensor_to_matrix!(
+    K_e::AbstractMatrix{Float64},
+    K_blocks::AbstractMatrix{Tensor{2,3,Float64,9}})
+
+    nnodes = size(K_blocks, 1)
+    for i in 1:nnodes, j in 1:nnodes
+        for α in 1:3, β in 1:3
+            K_e[3*(i-1)+α, 3*(j-1)+β] = K_blocks[i, j][α, β]
+        end
+    end
+    nothing
+end
+
+"""
+    compute_element_stiffness!(K_blocks, X, C, topology, basis, ips)
+
+Compute element stiffness (reused from continuum_3d.jl).
+
+See continuum_3d.jl for detailed documentation.
+"""
+function compute_element_stiffness!(
+    K_blocks::AbstractMatrix{Tensor{2,3,Float64,9}},
+    X::Vector{Vec{3,Float64}},
+    C::Tensor{4,3,Float64,81},
+    topology::T,
+    basis::B,
+    ips) where {T<:AbstractTopology{N},B<:AbstractBasis} where N
+
+    for k in 1:N, l in 1:N
+        for ip in ips
+            ξ = Vec{3}(ip.ξ)
+            w = ip.weight
+
+            dN_dξ = get_basis_derivatives(topology, basis, 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)
+
+            grad_k = J_inv_T ⋅ dN_dξ[k]
+            grad_l = J_inv_T ⋅ dN_dξ[l]
+
+            K_kl = compute_stiffness_block(grad_k, grad_l, C)
+
+            K_blocks[k, l] += K_kl * detJ * w
+        end
+    end
+
+    nothing
+end