Implement full 4th-order elasticity tensor approach in CPU backend:
- Fix topology extraction: extract_topology_type() returns type, then
instantiate with node count N (was causing crashes)
- Implement basis derivative evaluation: get_basis_derivatives() call
now works (BLOCKER resolved)
- Complete Jacobian transformation: J = ∑ X_k ⊗ dN_k/dξ using proper
tensor outer products (Tensors.jl)
- Implement stiffness assembly: K_ij^{αβ} = ∫ (∂N_i/∂x_γ) C_{αβγδ}
(∂N_j/∂x_δ) detJ dξ with double contractions
- Add basevec() helper for constructing unit vectors
NO B-matrix, NO Voigt notation - pure tensor mathematics following
golden standard (docs/src/book/multigpu_nodal_assembly.md).
This is the foundation for GPU implementation (same math, different backend).
- ElasticityDataCPU struct wraps ElementAssemblyData
- initialize_backend() assembles global system from immutable Elements
- compute_element_stiffness() uses Tensors.jl (blocked by get_basis_derivatives)
- cg_solve() implements Conjugate Gradient iterative solver
- Supports Dirichlet boundary conditions from Physics API
- 228 lines: Traditional element assembly approach for CPU
Jukka Aho