AI-Assisted Development of a Nonlinear Finite Element Analysis Program: A Case Study Using a Large Language Model

Abstract

This paper presents a structured human-AI collaborative workflow for developing verified scientific software from a published research paper. The large language model Claude (Anthropic) was guided by the author to translate, reimplement, and optimise a nonlinear finite element analysis (FEA) program originally published in 2015. The original program implemented a Combined Corotational-Total Lagrangian (CR-TL) formulation for large-displacement 2D beam structures in Microsoft Excel VBA. Using a domain-specific skill document and iterative prompt engineering, Claude generated an equivalent Python implementation. It subsequently identified six performance bottlenecks. The optimised implementation replaces dense matrix operations with sparse assembly, eliminates the Python element loop through vectorised NumPy einsum operations, and applies boundary conditions via a large-penalty method. Verification against NAFEMS benchmark tests NLGB2 and NLGB4 shows results matching closed-form solutions to four decimal places, with no parameter tuning or calibration. A 154-fold reduction in computation time at 1000 elements enables models with up to 5000 elements on a standard laptop. Three categories of LLM error are identified and characterised. The work demonstrates that domain-expert-guided AI collaboration can produce verified, production-quality scientific software from published numerical formulations.

Introduction

The text describes a study on using a large language model (Anthropic’s Claude) to redevelop and optimise a nonlinear finite element analysis (FEA) program for large-displacement beam structures, originally implemented in Excel VBA, into a high-performance Python library.

The motivation is that nonlinear FEA for problems like offshore pipeline installation requires accurate geometrically nonlinear modelling, but building such software is complex and demands deep expertise in mechanics, numerical methods, and software engineering. While LLMs (and tools like GitHub Copilot) are known to speed up general coding, their reliability in physics-heavy scientific computing remains uncertain, especially for tasks requiring strict numerical correctness.

The study reimplements a 2015 CR-TL-based corotational beam FEA program, validates it against NAFEMS benchmark problems, and uses a structured “skill document” plus human–AI collaboration workflow to guide development. The resulting Python version achieves a 154× performance improvement and scales to about 5000 elements.

Key findings are that:

• A domain-specific “skill document” is crucial for constraining LLM behaviour and encoding both equations and engineering judgement.
• Human expertise remains essential for decisions the LLM cannot reliably make (e.g., solver choice, rotation handling, parameter tuning).
• Mandatory benchmark verification is necessary because LLM-generated code can pass superficial tests while failing silently in critical cases.
• LLMs can significantly accelerate scientific software development but are unreliable without strong expert oversight.

The methodology is structured as an iterative loop: specification via skill document, staged code generation, benchmark-based verification, error categorisation, optimisation guided by profiling, and continuous documentation updates.

Error analysis shows typical LLM failure modes in scientific computing, including missing physics-critical variables (e.g., moment terms), incorrect rotation handling, and environment-dependent syntax issues that may not appear in basic tests.

Conclusion

This paper has demonstrated a structured human-AI collaborative workflow for producing verified, optimised scientific software from a published numerical formulation. Principal conclusions are as follows. 1) The skill document approach was the most important single methodological element. Encoding domain knowledge, engineering judgement, and verification criteria in a reusable reference document enabled consistent, high-quality LLM output across multiple sessions. 2) The Python implementation correctly reproduced the CR-TL formulation without calibration, matching closed-form solutions to four decimal places on both NLGB2 and NLGB4. 3) Six performance bottlenecks were identified by expert-directed profiling and resolved by the LLM, achieving a 154-fold speedup at 1000 elements through sparse matrices, vectorised einsum assembly, and a penalty BC method. 4) Three LLM error categories were characterised — omission, syntax compatibility, and solver strategy. Mandatory benchmark verification is the essential safeguard against all three, and is irreplaceable by code review or unit testing alone. 5) The methodology is generalisable to other published numerical methods with clear mathematical specifications and available benchmarks. The results establish that domain-expert-guided AI collaboration is a viable and efficient path to verified, production-quality scientific software — not a shortcut that trades correctness for speed, but a structured workflow that achieves both.

References

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Copyright

Copyright © 2026 Sreekanth Manakkattil Sivaraman. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.