Solver algorithms

Reference for the analysis types and backend algorithms femorph-solver ships. The user-guide section walks through how to drive each solver; this page lists the underlying algorithm and its sources.

Analysis types

• Static analysis
• Modal analysis
• Cyclic-symmetry modal analysis
• Transient analysis

Backends

• Linear-solver backends
• Eigen-solver backends

Quick reference table

Analysis	Entry point	Algorithm	Backend chain
Static analysis	Model.solve	Sparse direct factor + back-substitute	Linear-solver backends
Modal analysis	Model.modal_solve	Shift-invert Lanczos / block-Davidson / LOBPCG	Eigen-solver backends × Linear-solver backends
Cyclic-symmetry modal analysis	Model.cyclic_modal_solve	Per-harmonic real 2n-augmented Lanczos (Grimes-Lewis-Simon 1994)	Eigen-solver backends × Linear-solver backends
Transient analysis	Model.transient_solve() (roadmap) / modal-superposition (TA-14)	Newmark-β / generalised-α (direct); modal-superposition (decoupled SDOFs)	Linear-solver backends

How the dispatch chains plug together

• Linear-solver backends — one chain (Pardiso → CHOLMOD → MUMPS → UMFPACK → SuperLU) used by every analysis that factors a sparse matrix.

• Eigen-solver backends — modal / cyclic-modal pick ARPACK / PRIMME / LOBPCG. The shift-invert path inside the Lanczos / block-Davidson loop calls back into the linear chain, so the same Pardiso / CHOLMOD factor accelerates every shift-invert matrix-vector product.

See the per-chapter cite blocks for full algorithmic references.

See also

Solving — the user-facing how-to for each entry point.