A Constrained Natural-Language Interface for Variational Multi-Physics Finite Element Simulations in FEniCS

The article presents a constrained natural-language interface for variational multi-physics finite element simulations using the FEniCS framework, focusing on structured JSON parsing and Gmsh code generation for non-catalog geometries. The system employs a deterministic dispatcher that maps validated specifications to five human-written FEniCS/UFL templates, achieving sub-percent agreement with analytical solutions for smooth cases and 2-5 percent for nonlinear cases. This approach mitigates reliability risks associated with LLM-generated solver code, providing a robust solution for practitioners needing reliable finite element analysis without open-ended code generation.