Explains the correct pattern for matrix-vector products in Krylov methods:
- Fields accessed through element_set (not passed separately)
- GPU kernel computes y=K*x (not K itself)
- O(N) memory (vs O(N²) for stored matrix)
- Type-stable field access (compile-time types)
Key insights:
- GMRES needs matvec operation, not the matrix
- ElementSet contains elements + fields together
- Zero allocations with immutable connectivity/fields
- Natural pattern for contact mechanics (nodal updates)
- Material state separate from field parameters
Compares old vs new approach:
- Old: Dict{String,Any} in element (type-unstable)
- New: NamedTuple in ElementSet (type-stable)
- Old: O(N²) matrix storage
- New: O(N) matrix-free operator
Validated with gpu_elementset_matvec_demo.jl:
- GPU/CPU results match exactly
- Fields accessed naturally through element_set
- Returns y vector (what Krylov methods need)
Jukka Aho