Add extensive documentation for the basis module covering:
1. Architecture and design philosophy
- Separation of topology and basis
- Zero-cost abstraction principles
- SVector return types and dual-vector design
2. API overview and usage examples
- get_basis_functions() and get_basis_derivatives()
- nbasis() for compile-time basis function count
- Integration with topology and quadrature modules
3. Code generation system
- Vandermonde approach explained
- Symbolic differentiation and simplification
- Why offline generation vs runtime symbolic math
4. Extension guide
- Adding higher-order elements (step-by-step)
- Hierarchical and specialized bases
- When to use generator vs direct implementation
5. Performance characteristics
- Benchmarks: 100-1000× speedup over v0.5.1
- Zero allocations, subnanosecond evaluations
- Scaling with element order
6. Advanced topics
- Numerical precision and ill-conditioned Vandermonde
- Jacobian and physical derivatives
- Partition of unity and reproduction
- Integration accuracy requirements
Total: ~1800 lines of documentation with complete examples,
mathematical foundations, and practical guidance.
Jukka Aho