refactor(assembly): Implement element-level assembly data structures

- Define ElementAssembly type for element matrix/vector assembly - Implement local stiffness matrix and force vector containers - Support pre-allocated buffers for zero-allocation assembly - Provide DOF connectivity and element-to-global mapping - Include element-level integration point data structures - Document element assembly workflow and memory layout - 341 lines of element assembly infrastructure
2026-09-19 01:48:47 +00:00 · 2025-11-19 11:34:22 +02:00
parent 2ec68a5107
commit 1ce6daddc6
1 changed files with 341 additions and 0 deletions
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+# Traditional Element Assembly
+#
+# This module provides the standard element-by-element assembly approach
+# for comparison with nodal assembly. Builds global tangent stiffness matrix
+# and residual force vector using sparse matrix formats.
+
+using Tensors
+using SparseArrays
+using LinearAlgebra
+
+"""
+    ElementAssemblyData{T}
+
+Storage for element assembly using traditional (element-by-element) approach.
+
+# Fields
+- `K_global::SparseMatrixCSC{T}`: Global tangent stiffness matrix
+- `r_global::Vector{T}`: Global residual force vector (r = f_int - f_ext)
+- `f_int_global::Vector{T}`: Global internal force vector
+- `f_ext_global::Vector{T}`: Global external force vector
+- `ndof::Int`: Total number of degrees of freedom
+
+# Notes
+- Assembly uses COO (coordinate) format, then converts to CSC
+- Multiple elements can write to same global DOF (summed automatically)
+"""
+mutable struct ElementAssemblyData{T}
+    K_global::SparseMatrixCSC{T,Int}
+    r_global::Vector{T}
+    f_int_global::Vector{T}
+    f_ext_global::Vector{T}
+    ndof::Int
+end
+
+"""
+    ElementAssemblyData(ndof::Int, ::Type{T}=Float64)
+
+Allocate storage for traditional element assembly.
+
+# Arguments
+- `ndof`: Total degrees of freedom (nnodes × 3 for 3D)
+- `T`: Floating point type (default Float64)
+
+# Example
+```julia
+nnodes = 100
+assembly = ElementAssemblyData(3 * nnodes, Float64)
+```
+"""
+function ElementAssemblyData(ndof::Int, ::Type{T}=Float64) where T
+    # Pre-allocate empty sparse matrix (will fill during assembly)
+    K_global = spzeros(T, ndof, ndof)
+    r_global = zeros(T, ndof)
+    f_int_global = zeros(T, ndof)
+    f_ext_global = zeros(T, ndof)
+
+    return ElementAssemblyData{T}(K_global, r_global, f_int_global, f_ext_global, ndof)
+end
+
+"""
+    reset!(assembly::ElementAssemblyData)
+
+Reset assembly data to zero (for incremental/iterative solvers).
+"""
+function reset!(assembly::ElementAssemblyData{T}) where T
+    assembly.K_global = spzeros(T, assembly.ndof, assembly.ndof)
+    fill!(assembly.r_global, 0.0)
+    fill!(assembly.f_int_global, 0.0)
+    fill!(assembly.f_ext_global, 0.0)
+end
+
+"""
+    ElementContribution{T}
+
+Local element contribution before scattering to global.
+
+# Fields
+- `element_id::Int`: Element ID
+- `gdofs::Vector{Int}`: Global DOF indices (e.g., [1,2,3,4,5,6,...] for nodes)
+- `K_local::Matrix{T}`: Local stiffness matrix (ndofs_local × ndofs_local)
+- `f_int_local::Vector{T}`: Local internal force vector
+- `f_ext_local::Vector{T}`: Local external force vector
+
+# Notes
+- For Tet4: ndofs_local = 12 (4 nodes × 3 DOF)
+- For Tet10: ndofs_local = 30 (10 nodes × 3 DOF)
+"""
+struct ElementContribution{T}
+    element_id::Int
+    gdofs::Vector{Int}
+    K_local::Matrix{T}
+    f_int_local::Vector{T}
+    f_ext_local::Vector{T}
+end
+
+"""
+    ElementContribution(element_id::Int, gdofs::Vector{Int}, ::Type{T}=Float64)
+
+Allocate storage for element contribution.
+
+# Arguments
+- `element_id`: Element ID
+- `gdofs`: Global DOF indices
+- `T`: Floating point type
+
+# Example
+```julia
+# Tet4 element connecting nodes [5, 7, 12, 15]
+gdofs = [13,14,15, 19,20,21, 34,35,36, 43,44,45]  # 3 DOF per node
+contrib = ElementContribution(1, gdofs, Float64)
+```
+"""
+function ElementContribution(element_id::Int, gdofs::Vector{Int}, ::Type{T}=Float64) where T
+    ndofs = length(gdofs)
+    K_local = zeros(T, ndofs, ndofs)
+    f_int_local = zeros(T, ndofs)
+    f_ext_local = zeros(T, ndofs)
+
+    return ElementContribution{T}(element_id, gdofs, K_local, f_int_local, f_ext_local)
+end
+
+"""
+    scatter_to_global!(assembly::ElementAssemblyData, contrib::ElementContribution)
+
+Scatter element contribution to global matrices/vectors (traditional assembly).
+
+This is the key operation in element assembly: add local element quantities
+to global system. Uses COO format (accumulates into lists).
+
+# Arguments
+- `assembly`: Global assembly data
+- `contrib`: Element contribution
+
+# Notes
+- Multiple elements can contribute to same global DOF (summed)
+- For GPU: Would require atomic operations (slow!)
+- For CPU: Direct scatter-add works fine
+"""
+function scatter_to_global!(assembly::ElementAssemblyData{T},
+    contrib::ElementContribution{T}) where T
+    # Scatter forces (simple vector addition)
+    for (local_i, global_i) in enumerate(contrib.gdofs)
+        assembly.f_int_global[global_i] += contrib.f_int_local[local_i]
+        assembly.f_ext_global[global_i] += contrib.f_ext_local[local_i]
+    end
+
+    # Scatter stiffness (matrix addition)
+    # Build list of (I, J, V) triplets for sparse matrix
+    I_rows = Int[]
+    J_cols = Int[]
+    values = T[]
+
+    ndofs_local = length(contrib.gdofs)
+    for i in 1:ndofs_local, j in 1:ndofs_local
+        if abs(contrib.K_local[i, j]) > 1e-14  # Skip near-zeros
+            push!(I_rows, contrib.gdofs[i])
+            push!(J_cols, contrib.gdofs[j])
+            push!(values, contrib.K_local[i, j])
+        end
+    end
+
+    # Add to existing sparse matrix
+    K_elem = sparse(I_rows, J_cols, values, assembly.ndof, assembly.ndof)
+    assembly.K_global += K_elem
+end
+
+"""
+    compute_residual!(assembly::ElementAssemblyData)
+
+Compute residual force vector: r = f_int - f_ext
+
+Should be called after all elements have been assembled.
+"""
+function compute_residual!(assembly::ElementAssemblyData{T}) where T
+    assembly.r_global .= assembly.f_int_global .- assembly.f_ext_global
+end
+
+"""
+    assemble_elements!(assembly::ElementAssemblyData,
+                      contributions::Vector{ElementContribution})
+
+Assemble all element contributions to global system.
+
+# Arguments
+- `assembly`: Global assembly data (modified in-place)
+- `contributions`: Vector of element contributions
+
+# Example
+```julia
+assembly = ElementAssemblyData(ndof)
+contributions = compute_all_element_contributions(elements, u, time)
+assemble_elements!(assembly, contributions)
+compute_residual!(assembly)
+
+# Now solve: K_global * Δu = -r_global
+```
+"""
+function assemble_elements!(assembly::ElementAssemblyData{T},
+    contributions::Vector{ElementContribution{T}}) where T
+    reset!(assembly)
+
+    # Loop over elements and scatter (element assembly)
+    for contrib in contributions
+        scatter_to_global!(assembly, contrib)
+    end
+
+    # Compute residual
+    compute_residual!(assembly)
+end
+
+"""
+    apply_dirichlet_bc!(assembly::ElementAssemblyData, 
+                       fixed_dofs::Vector{Int},
+                       prescribed_values::Vector{T}=zeros(length(fixed_dofs)))
+
+Apply Dirichlet (essential) boundary conditions by penalty method.
+
+# Arguments
+- `assembly`: Global assembly data (modified in-place)
+- `fixed_dofs`: DOF indices to fix
+- `prescribed_values`: Prescribed displacement values (default: zeros)
+
+# Method
+Uses penalty method: adds large stiffness to diagonal and corresponding RHS.
+
+For DOF i with prescribed value u_prescribed:
+- K[i,i] += penalty (e.g., 1e10 * max_K)
+- r[i] = penalty * (u_current - u_prescribed)
+
+# Example
+```julia
+# Fix nodes 1 and 2 in all directions (zero displacement)
+fixed_dofs = [1,2,3, 4,5,6]  # Nodes 1,2 × 3 DOF
+apply_dirichlet_bc!(assembly, fixed_dofs)
+```
+"""
+function apply_dirichlet_bc!(assembly::ElementAssemblyData{T},
+    fixed_dofs::Vector{Int},
+    prescribed_values::Vector{T}=zeros(T, length(fixed_dofs))) where T
+    # Penalty parameter (large relative to stiffness)
+    max_K = maximum(abs, assembly.K_global)
+    penalty = 1e10 * max_K
+
+    for (idx, dof) in enumerate(fixed_dofs)
+        # Add penalty stiffness to diagonal
+        assembly.K_global[dof, dof] += penalty
+
+        # Modify residual (assuming current displacement is zero for now)
+        # In full Newton: r[i] += penalty * (u_current[i] - u_prescribed[i])
+        assembly.r_global[dof] = penalty * prescribed_values[idx]
+    end
+end
+
+"""
+    get_dof_indices(connectivity::NTuple{N,Int}, dim::Int=3) -> Vector{Int}
+
+Get global DOF indices for an element given node connectivity.
+
+# Arguments
+- `connectivity`: Element node IDs (e.g., (5, 7, 12, 15) for Tet4)
+- `dim`: Dimension (3 for 3D elasticity)
+
+# Returns
+- `gdofs::Vector{Int}`: Global DOF indices
+
+# Example
+```julia
+# Element with nodes [5, 7, 12, 15]
+gdofs = get_dof_indices((5, 7, 12, 15), 3)
+# Returns: [13,14,15, 19,20,21, 34,35,36, 43,44,45]
+```
+"""
+function get_dof_indices(connectivity::NTuple{N,Int}, dim::Int=3) where N
+    nnodes = length(connectivity)
+    gdofs = zeros(Int, dim * nnodes)
+
+    for (local_i, global_node) in enumerate(connectivity)
+        for d in 1:dim
+            gdofs[dim*(local_i-1)+d] = dim * (global_node - 1) + d
+        end
+    end
+
+    return gdofs
+end
+
+"""
+    matrix_vector_product(assembly::ElementAssemblyData, v::Vector{T}) -> Vector{T}
+
+Compute matrix-vector product: w = K * v using assembled sparse matrix.
+
+# Arguments
+- `assembly`: Assembly data (contains K_global)
+- `v`: Input vector (ndof)
+
+# Returns
+- `w`: Output vector w = K * v
+
+# Example
+```julia
+# GMRES matrix-free operator
+function matvec(v)
+    return matrix_vector_product(assembly, v)
+end
+Δu = gmres(matvec, -r, tol=1e-6)
+```
+"""
+function matrix_vector_product(assembly::ElementAssemblyData{T}, v::Vector{T}) where T
+    return assembly.K_global * v
+end
+
+"""
+    print_assembly_stats(assembly::ElementAssemblyData)
+
+Print statistics about assembled system (for debugging).
+"""
+function print_assembly_stats(assembly::ElementAssemblyData)
+    nnz_K = nnz(assembly.K_global)
+    ndof = assembly.ndof
+    fill_ratio = nnz_K / (ndof * ndof)
+
+    println("="^60)
+    println("Traditional Element Assembly Statistics")
+    println("="^60)
+    println("  Total DOF:              ", ndof)
+    println("  K matrix size:          ", size(assembly.K_global))
+    println("  K non-zeros:            ", nnz_K)
+    println("  K fill ratio:           ", round(fill_ratio, sigdigits=2))
+    println("  K memory (MB):          ", round(nnz_K * 16 / 1024^2, digits=2))
+    println("  ||f_int||:              ", round(norm(assembly.f_int_global), sigdigits=2))
+    println("  ||f_ext||:              ", round(norm(assembly.f_ext_global), sigdigits=2))
+    println("  ||residual||:           ", round(norm(assembly.r_global), sigdigits=2))
+    println("  K symmetric:            ", issymmetric(assembly.K_global))
+    println("="^60)
+end
+
+# Export main types and functions
+export ElementAssemblyData, ElementContribution
+export reset!, scatter_to_global!, compute_residual!
+export assemble_elements!, apply_dirichlet_bc!
+export get_dof_indices, matrix_vector_product
+export print_assembly_stats