mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-09-19 01:48:47 +00:00
Jukka Aho
7b875dd117
- Tests NodeToElementsMap inverse connectivity (node → elements touching it)
- Validates "spider" pattern: set of nodes coupled to given node via shared elements
- Simple Tet4 mesh: 2 elements sharing face, tests node-element relationships
- Spider coupling patterns: corner nodes (1 element), shared nodes (2 elements)
- NodalStiffnessContribution storage: K_blocks (3×3 tensors), f_int, f_ext (Vec{3})
- Matrix-vector product: w_i = ∑_j K_ij ⊡ u_j (nodal assembly operation)
- Spider efficiency check: 2×2×2 hex mesh shows sparse coupling
- Corner node: 8 couplings
- Center node: 27 couplings (max for structured mesh)
- Key insight: only compute non-zero blocks (not full 81×81 matrix)
- Diagnostic output showing spider structure and coupling patterns
- 208 lines validating nodal assembly infrastructure with Tensors.jl
209 lines
6.9 KiB
Julia
209 lines
6.9 KiB
Julia
# Test nodal assembly data structures
|
||
#
|
||
# Demonstrates the "spider" pattern and inverse mapping for nodal assembly
|
||
|
||
using Test
|
||
using Tensors
|
||
|
||
include("../src/nodal_assembly_structures.jl")
|
||
|
||
@testset "Nodal Assembly Structures" begin
|
||
|
||
@testset "Simple Tet4 Mesh - 2 Elements" begin
|
||
# Two tetrahedra sharing a face (nodes 2,3,4)
|
||
#
|
||
# 5
|
||
# /|\
|
||
# / | \
|
||
# / | \
|
||
# 1---2---4
|
||
# \ | /
|
||
# \ | /
|
||
# \|/
|
||
# 3
|
||
#
|
||
# Element 1: nodes (1,2,3,4)
|
||
# Element 2: nodes (2,3,4,5)
|
||
|
||
connectivity = [
|
||
(1, 2, 3, 4), # Element 1
|
||
(2, 3, 4, 5) # Element 2
|
||
]
|
||
|
||
# Build inverse mapping
|
||
map = NodeToElementsMap(connectivity)
|
||
|
||
@test map.nnodes == 5
|
||
@test map.nelements == 2
|
||
|
||
# Node 1: only in element 1
|
||
@test length(map.node_to_elements[1]) == 1
|
||
@test map.node_to_elements[1][1].element_id == 1
|
||
@test map.node_to_elements[1][1].local_node_idx == 1
|
||
|
||
# Node 2: in both elements
|
||
@test length(map.node_to_elements[2]) == 2
|
||
@test map.node_to_elements[2][1].element_id == 1
|
||
@test map.node_to_elements[2][1].local_node_idx == 2
|
||
@test map.node_to_elements[2][2].element_id == 2
|
||
@test map.node_to_elements[2][2].local_node_idx == 1
|
||
|
||
# Node 5: only in element 2
|
||
@test length(map.node_to_elements[5]) == 1
|
||
@test map.node_to_elements[5][1].element_id == 2
|
||
@test map.node_to_elements[5][1].local_node_idx == 4
|
||
end
|
||
|
||
@testset "Node Spider - Coupling Pattern" begin
|
||
connectivity = [
|
||
(1, 2, 3, 4),
|
||
(2, 3, 4, 5)
|
||
]
|
||
|
||
map = NodeToElementsMap(connectivity)
|
||
|
||
# Node 1 spider: only element 1 touches it
|
||
spider_1 = get_node_spider(map, 1, connectivity)
|
||
@test spider_1 == [1, 2, 3, 4]
|
||
@test length(spider_1) == 4 # 4 nodes in spider → 4×3x3 blocks
|
||
|
||
# Node 2 spider: both elements touch it
|
||
spider_2 = get_node_spider(map, 2, connectivity)
|
||
@test spider_2 == [1, 2, 3, 4, 5] # Union of both elements
|
||
@test length(spider_2) == 5 # 5 nodes in spider → 5×3x3 blocks
|
||
|
||
# Node 3 spider: both elements
|
||
spider_3 = get_node_spider(map, 3, connectivity)
|
||
@test spider_3 == [1, 2, 3, 4, 5]
|
||
|
||
# Node 5 spider: only element 2
|
||
spider_5 = get_node_spider(map, 5, connectivity)
|
||
@test spider_5 == [2, 3, 4, 5]
|
||
@test length(spider_5) == 4
|
||
end
|
||
|
||
@testset "NodalStiffnessContribution - Storage" begin
|
||
connectivity = [(1, 2, 3, 4)]
|
||
map = NodeToElementsMap(connectivity)
|
||
spider = get_node_spider(map, 1, connectivity)
|
||
|
||
# Allocate contribution storage
|
||
contrib = NodalStiffnessContribution(1, spider, Float64)
|
||
|
||
@test contrib.node_id == 1
|
||
@test contrib.spider_nodes == [1, 2, 3, 4]
|
||
@test length(contrib.K_blocks) == 4
|
||
@test all(iszero, contrib.K_blocks) # Initially zero
|
||
@test iszero(contrib.f_int)
|
||
@test iszero(contrib.f_ext)
|
||
|
||
# Verify types (Tensors.jl)
|
||
@test contrib.K_blocks[1] isa Tensor{2,3,Float64,9}
|
||
@test contrib.f_int isa Vec{3,Float64}
|
||
@test contrib.f_ext isa Vec{3,Float64}
|
||
end
|
||
|
||
@testset "Matrix-Vector Product - Nodal" begin
|
||
# Simple 2-node problem for testing
|
||
connectivity = [(1, 2, 3, 4)]
|
||
map = NodeToElementsMap(connectivity)
|
||
spider = get_node_spider(map, 1, connectivity)
|
||
|
||
contrib = NodalStiffnessContribution(1, spider, Float64)
|
||
|
||
# Fill in some test stiffness blocks
|
||
# K_11 = identity (self-coupling)
|
||
contrib.K_blocks[1] = one(Tensor{2,3,Float64})
|
||
|
||
# K_12 = simple coupling
|
||
contrib.K_blocks[2] = Tensor{2,3}((2.0, 0.0, 0.0,
|
||
0.0, 2.0, 0.0,
|
||
0.0, 0.0, 2.0))
|
||
|
||
# K_13, K_14 = zero (no coupling for this test)
|
||
contrib.K_blocks[3] = zero(Tensor{2,3,Float64})
|
||
contrib.K_blocks[4] = zero(Tensor{2,3,Float64})
|
||
|
||
# Displacement field
|
||
u = [
|
||
Vec{3}((1.0, 2.0, 3.0)), # u_1
|
||
Vec{3}((0.5, 0.5, 0.5)), # u_2
|
||
Vec{3}((0.0, 0.0, 0.0)), # u_3
|
||
Vec{3}((0.0, 0.0, 0.0)) # u_4
|
||
]
|
||
|
||
# Matrix-vector product at node 1
|
||
w_1 = matrix_vector_product_nodal(contrib, u)
|
||
|
||
# Expected: w_1 = K_11*u_1 + K_12*u_2
|
||
# = [1 0 0; 0 1 0; 0 0 1] * [1,2,3] + [2 0 0; 0 2 0; 0 0 2] * [0.5,0.5,0.5]
|
||
# = [1,2,3] + [1,1,1] = [2,3,4]
|
||
|
||
expected = Vec{3}((2.0, 3.0, 4.0))
|
||
@test w_1 ≈ expected
|
||
end
|
||
|
||
@testset "Spider Efficiency Check" begin
|
||
# Larger mesh to show efficiency
|
||
# Hex8 mesh: 2×2×2 elements = 27 nodes
|
||
# Build connectivity for structured hex mesh
|
||
connectivity = Vector{NTuple{8,Int}}()
|
||
|
||
node_id(i, j, k) = 1 + i + 3 * j + 9 * k # 3×3×3 grid
|
||
|
||
for iz in 0:1, iy in 0:1, ix in 0:1
|
||
push!(connectivity, (
|
||
node_id(ix, iy, iz),
|
||
node_id(ix + 1, iy, iz),
|
||
node_id(ix + 1, iy + 1, iz),
|
||
node_id(ix, iy + 1, iz),
|
||
node_id(ix, iy, iz + 1),
|
||
node_id(ix + 1, iy, iz + 1),
|
||
node_id(ix + 1, iy + 1, iz + 1),
|
||
node_id(ix, iy + 1, iz + 1)
|
||
))
|
||
end
|
||
|
||
map = NodeToElementsMap(connectivity)
|
||
@test map.nelements == 8
|
||
|
||
# Corner node: touches 1 element
|
||
corner_node = node_id(0, 0, 0)
|
||
spider_corner = get_node_spider(map, corner_node, connectivity)
|
||
@test length(spider_corner) == 8 # Only nodes in 1 hex
|
||
|
||
# Center node: touches 8 elements
|
||
center_node = node_id(1, 1, 1)
|
||
spider_center = get_node_spider(map, center_node, connectivity)
|
||
@test length(spider_center) == 27 # All nodes in mesh!
|
||
|
||
# Edge node: touches fewer elements
|
||
edge_node = node_id(1, 0, 0)
|
||
spider_edge = get_node_spider(map, edge_node, connectivity)
|
||
@test 8 < length(spider_edge) < 27 # Intermediate
|
||
|
||
println("\nSpider sizes for 2×2×2 hex mesh (27 nodes):")
|
||
println(" Corner node: $(length(spider_corner)) couplings")
|
||
println(" Edge node: $(length(spider_edge)) couplings")
|
||
println(" Center node: $(length(spider_center)) couplings")
|
||
println("\nKey insight: We only compute non-zero blocks!")
|
||
println(" Full matrix would be 81×81 (27 nodes × 3 DOF)")
|
||
println(" But most nodes have < 27 couplings")
|
||
end
|
||
|
||
@testset "Diagnostic Output" begin
|
||
connectivity = [
|
||
(1, 2, 3, 4),
|
||
(2, 3, 4, 5)
|
||
]
|
||
|
||
map = NodeToElementsMap(connectivity)
|
||
|
||
println("\n" * "="^60)
|
||
println("DIAGNOSTIC: Spider pattern for node 2 (shared by 2 elements)")
|
||
println("="^60)
|
||
print_spider_info(map, 2, connectivity)
|
||
println("="^60)
|
||
end
|
||
end
|