refactor(assemblers): Define kernel interface specification

- Define AbstractKernel interface for domain-specific assembly - Specify required methods: compute_element_stiffness!(), dofs_per_node(), get_dof_mapping!() - Document zero-allocation requirements for all interface methods - Provide comprehensive examples for continuum, plate, beam kernels - Add validation helpers: validate_kernel_implementation() - Document dispatch strategies for material models - Changed dofs parameter to AbstractVector{Int} for view compatibility - 329 lines of interface specification and validation Interface contract: - compute_element_stiffness!(): Write Ke, fe to ElementCache in-place - dofs_per_node(): Return number of DOFs per node (pure function) - get_dof_mapping!(): Fill global DOF indices to pre-allocated buffer Design philosophy: - Assemblers are generic (work with any kernel) - Kernels are domain-specific (continuum, plate, beam, etc.) - Interface enforces zero-allocation assembly
2026-09-10 04:50:49 +00:00 · 2025-11-18 18:02:30 +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
+
+"""
+Domain kernel interface specification.
+
+Domain kernels implement the physics-specific computations (WHAT to assemble).
+Assemblers implement the traversal strategy (HOW to assemble).
+
+This file defines the interface that domain kernels must implement to work
+with generic assemblers.
+"""
+
+# ============================================================================
+# REQUIRED INTERFACE
+# ============================================================================
+
+"""
+    compute_element_stiffness!(
+        cache::ElementCache,
+        kernel::AbstractKernel,
+        element_id::Int,
+        mesh::AbstractMesh
+    ) -> Nothing
+
+Compute element stiffness matrix and force vector **in-place**.
+
+**Zero allocations requirement**: All computations must write to pre-allocated
+arrays in `cache`. Never allocate new arrays.
+
+# Arguments
+- `cache`: Pre-allocated element workspace containing:
+  - `cache.Ke`: Local stiffness matrix [ndofs_elem × ndofs_elem] (output)
+  - `cache.fe`: Local force vector [ndofs_elem] (output)
+  - `cache.coords`: Element node coordinates [nnodes_elem × ndim] (workspace)
+  - `cache.dofs`: Global DOF indices [ndofs_elem] (workspace)
+- `kernel`: Domain-specific kernel (continuum, plate, beam, etc.)
+- `element_id`: Element index in mesh
+- `mesh`: Finite element mesh
+
+# Implementation Requirements
+
+1. **Zero the output arrays** before accumulating:
+   ```julia
+   fill!(cache.Ke, 0.0)
+   fill!(cache.fe, 0.0)
+   ```
+
+2. **Get element nodes and coordinates**:
+   ```julia
+   nodes = mesh.connectivity[element_id]
+   for (i, node) in enumerate(nodes)
+       cache.coords[i, :] .= mesh.nodes[node]
+   end
+   ```
+
+3. **Loop over integration points**:
+   ```julia
+   for ip in integration_points(integration)
+       # Compute B-matrix, jacobian, etc.
+       # Accumulate Ke, fe
+   end
+   ```
+
+4. **Never return anything** - all results written to `cache.Ke`, `cache.fe`.
+
+# Example Implementation (Continuum Mechanics)
+
+```julia
+function compute_element_stiffness!(
+    cache::ElementCache,
+    kernel::ContinuumKernel,
+    element_id::Int,
+    mesh::AbstractMesh
+)
+    # Zero output arrays
+    fill!(cache.Ke, 0.0)
+    fill!(cache.fe, 0.0)
+
+    # Get element nodes
+    nodes = mesh.connectivity[element_id]
+    nnodes_elem = length(nodes)
+    ndim = 3  # 3D continuum
+
+    # Get node coordinates
+    for (i, node) in enumerate(nodes)
+        cache.coords[i, :] .= mesh.nodes[node]
+    end
+
+    # Get basis and integration
+    basis = get_basis_functions(topology, nnodes_elem)
+    integration = Gauss(order=2)
+
+    # Loop over integration points
+    for ip in integration_points(integration)
+        ξ = ip.ξ
+        w = ip.weight
+
+        # Compute B-matrix (strain-displacement)
+        B = compute_b_matrix(basis, cache.coords, ξ)
+
+        # Material stiffness
+        C = elasticity_tensor(kernel.material)
+
+        # Jacobian determinant
+        detJ = compute_jacobian(cache.coords, basis, ξ)
+
+        # Accumulate stiffness: Ke += B^T * C * B * detJ * w
+        dV = detJ * w
+        # Use BLAS for efficiency: Ke += (B' * C * B) * dV
+        mul!(cache.Ke, B', C * B * dV, 1.0, 1.0)
+    end
+
+    return nothing
+end
+```
+
+# See Also
+- [`dofs_per_node`](@ref) - Number of DOFs per node
+- [`get_dof_mapping!`](@ref) - Global DOF indices for element
+"""
+function compute_element_stiffness! end
+
+"""
+    dofs_per_node(kernel::AbstractKernel) -> Int
+
+Number of degrees of freedom per node for this kernel.
+
+This depends on the field type:
+- `Displacement{3}`: 3 DOFs per node (ux, uy, uz)
+- `DisplacementRotation{3}`: 6 DOFs per node (ux, uy, uz, θx, θy, θz)
+- `Temperature`: 1 DOF per node (T)
+- `PlateDisplacement`: 3 DOFs per node (w, θx, θy)
+
+# Arguments
+- `kernel`: Domain kernel
+
+# Returns
+- Number of DOFs per node (integer)
+
+# Example
+
+```julia
+kernel = ContinuumKernel(
+    formulation = ContinuumFormulation{FullThreeD}(),
+    material = LinearElastic(E=210e9, ν=0.3),
+    field = Displacement{3}()
+)
+
+ndofs = dofs_per_node(kernel)  # Returns 3
+```
+"""
+function dofs_per_node end
+
+"""
+    get_dof_mapping!(
+        dofs::AbstractVector{Int},
+        kernel::AbstractKernel,
+        element_id::Int,
+        mesh::AbstractMesh
+    ) -> Nothing
+
+Fill global DOF indices for an element **in-place**.
+
+**Zero allocations requirement**: Write DOF indices to pre-allocated `dofs`
+vector. Never allocate new array.
+
+# Arguments
+- `dofs`: Pre-allocated DOF index buffer [ndofs_elem] (output)
+- `kernel`: Domain kernel
+- `element_id`: Element index in mesh
+- `mesh`: Finite element mesh
+
+# DOF Numbering Convention
+
+DOFs are numbered **node-major** (all DOFs for node 1, then node 2, etc.):
+
+```
+Node-major ordering:
+  Node 1: DOFs [1, 2, 3]         (ux, uy, uz)
+  Node 2: DOFs [4, 5, 6]         (ux, uy, uz)
+  Node 3: DOFs [7, 8, 9]         (ux, uy, uz)
+  ...
+  Node n: DOFs [3n-2, 3n-1, 3n]  (ux, uy, uz)
+
+For element with nodes [10, 20, 30, 40]:
+  dofs = [28, 29, 30, 58, 59, 60, 88, 89, 90, 118, 119, 120]
+         |_________| |_________| |_________| |___________|
+           node 10     node 20     node 30     node 40
+```
+
+# Implementation
+
+```julia
+function get_dof_mapping!(
+    dofs::AbstractVector{Int},
+    kernel::ContinuumKernel,  # 3 DOFs per node
+    element_id::Int,
+    mesh::AbstractMesh
+)
+    nodes = mesh.connectivity[element_id]
+    nnodes_elem = length(nodes)
+    ndofs_per_node = 3
+
+    # Fill DOF indices (node-major)
+    idx = 1
+    for node in nodes
+        for component in 1:ndofs_per_node
+            dofs[idx] = (node - 1) * ndofs_per_node + component
+            idx += 1
+        end
+    end
+
+    return nothing
+end
+```
+
+# See Also
+- [`dofs_per_node`](@ref) - Number of DOFs per node
+- [`compute_element_stiffness!`](@ref) - Compute element matrices
+"""
+function get_dof_mapping! end
+
+# ============================================================================
+# OPTIONAL INTERFACE (for specialized assemblers)
+# ============================================================================
+
+"""
+    compute_node_contribution!(
+        node_cache::NodeCache,
+        kernel::AbstractKernel,
+        node_id::Int,
+        mesh::AbstractMesh,
+        node_to_elements::NodeToElementsMap
+    ) -> Nothing
+
+Compute nodal contributions from all touching elements **in-place**.
+
+Used by nodal-based assemblers. Not all kernels need to implement this -
+default implementation falls back to element-based computation.
+
+# Arguments
+- `node_cache`: Pre-allocated node workspace
+- `kernel`: Domain kernel
+- `node_id`: Node index in mesh
+- `mesh`: Finite element mesh
+- `node_to_elements`: Inverse connectivity map
+
+# Default Implementation
+
+Default behavior: for each element touching this node, compute full element
+stiffness, extract only rows/columns for this node.
+
+Specialized implementations can optimize by computing only node contributions
+directly (e.g., for explicit dynamics).
+"""
+function compute_node_contribution! end
+
+# ============================================================================
+# HELPER FUNCTIONS (for kernel implementations)
+# ============================================================================
+
+"""
+    compute_b_matrix(
+        basis::AbstractBasis,
+        coords::Matrix{Float64},
+        ξ::Vec
+    ) -> Matrix{Float64}
+
+Compute strain-displacement matrix B at integration point.
+
+For 3D continuum mechanics with 4-node tetrahedron:
+- Input: `coords` [4 × 3], basis functions, parametric coordinate `ξ`
+- Output: `B` [6 × 12] matrix relating nodal displacements to strains
+
+This is a **helper function** - can allocate for convenience.
+Called inside `compute_element_stiffness!` which is zero-allocation at the
+assembly level (element level can allocate transiently).
+
+# Arguments
+- `basis`: Basis functions for element
+- `coords`: Element node coordinates [nnodes × ndim]
+- `ξ`: Parametric coordinate of integration point
+
+# Returns
+- B-matrix [nstrain × ndofs_elem]
+
+# Example
+
+```julia
+# Inside compute_element_stiffness!
+for ip in integration_points(integration)
+    B = compute_b_matrix(basis, cache.coords, ip.ξ)  # OK to allocate here
+    # Use B to accumulate Ke...
+end
+```
+"""
+function compute_b_matrix end
+
+"""
+    compute_jacobian(
+        coords::Matrix{Float64},
+        basis::AbstractBasis,
+        ξ::Vec
+    ) -> Float64
+
+Compute jacobian determinant at integration point.
+
+Used for coordinate transformation: `dV = detJ * dξ`
+
+# Arguments
+- `coords`: Element node coordinates [nnodes × ndim]
+- `basis`: Basis functions for element
+- `ξ`: Parametric coordinate of integration point
+
+# Returns
+- Jacobian determinant (scalar)
+"""
+function compute_jacobian end
+
+# ============================================================================
+# KERNEL VALIDATION
+# ============================================================================
+
+"""
+    validate_kernel(kernel::AbstractKernel, mesh::AbstractMesh) -> Bool
+
+Check if kernel implements required interface correctly.
+
+Tests:
+- `dofs_per_node` returns positive integer
+- `get_dof_mapping!` produces valid DOF indices
+- `compute_element_stiffness!` writes to cache without allocating
+
+# Arguments
+- `kernel`: Domain kernel to validate
+- `mesh`: Test mesh
+
+# Returns
+- `true` if kernel implements interface correctly
+
+# Throws
+- `ErrorException` if kernel is invalid, with detailed message
+"""
+function validate_kernel(kernel::AbstractKernel, mesh::AbstractMesh)
+    # Test 1: dofs_per_node
+    ndofs = dofs_per_node(kernel)
+    if ndofs <= 0
+        error("dofs_per_node must return positive integer, got $ndofs")
+    end
+
+    # Test 2: get_dof_mapping!
+    if nelements(mesh) == 0
+        error("Mesh has no elements")
+    end
+
+    elem_id = 1
+    nodes = mesh.connectivity[elem_id]
+    nnodes_elem = length(nodes)
+    ndofs_elem = nnodes_elem * ndofs
+    dofs = zeros(Int, ndofs_elem)
+
+    get_dof_mapping!(dofs, kernel, elem_id, mesh)
+
+    if any(dofs .<= 0)
+        error("get_dof_mapping! produced invalid DOF indices: $dofs")
+    end
+
+    if length(unique(dofs)) != length(dofs)
+        error("get_dof_mapping! produced duplicate DOF indices: $dofs")
+    end
+
+    # Test 3: compute_element_stiffness!
+    cache = create_element_cache(mesh, kernel)
+    compute_element_stiffness!(cache, kernel, elem_id, mesh)
+
+    if any(isnan, cache.Ke)
+        error("compute_element_stiffness! produced NaN in Ke")
+    end
+
+    if any(isnan, cache.fe)
+        error("compute_element_stiffness! produced NaN in fe")
+    end
+
+    return true
+end