Eighty Years of the Finite Element Method (2022)

Original Article ↗ Hacker News Discussion ↗

State of the FEM/FEA Industry

  • Many practitioners feel everyday FEM practice has stagnated: workflows and tools (ANSYS, NASTRAN, Abaqus) look much like they did 10–20 years ago.
  • Some describe commercial ecosystems as sales-driven “muddy death marches” with frequent licensing reshuffles and product killing to upsell tiers.
  • Others push back, citing advances such as contact elements, bolt preload, detailed composite modeling, progressive failure, thin-layer modeling, and optimization as meaningful progress.
  • COMSOL is seen as a major “new” player, though it has existed for decades; valued mainly for easy multi-physics coupling rather than best-in-class single-physics solvers.

Commercial vs Open-Source Tools

  • Dominant commercial tools mentioned: ANSYS, Abaqus, NASTRAN, LS-DYNA, COMSOL.
  • COMSOL praised for meshing, integrated geometry, scripting, and multi-physics coupling; criticism that individual physics modules are weaker than specialist tools.
  • Open-source landscape seen as fragmented and immature for industry-grade multiphysics:
    • Structural/thermal: CalculiX (buggy), Code_Aster (powerful but confusing), open NASTRAN forks.
    • PDE frameworks: FEniCS, deal.II, SELF; mostly academic, require coding.
    • CFD/fluids: OpenFOAM (powerful but “impenetrable” to newcomers), plus mentions of Elmer and OpenRadioss.
  • FreeCAD and Gmsh used as CAD/meshing front-ends; FEATool offers a GUI atop FEniCS.

Workflows, Use Cases, and Accessibility

  • Typical engineering workflow: CAD (e.g., SolidWorks) → meshing/FEA → iteration → prototype → further iteration.
  • For hobbyists, full CAD–mesh–solve–postprocess pipeline is described as a high barrier to entry.
  • Example hobby/industry domains: electronics/EMI, antennas, aerodynamics, rocketry, machining, robotics, 3D-printing/topology optimization, graphics.

Understanding and Teaching FEM

  • Several participants find deriving FEM via Galerkin/variational methods difficult; others outline a conceptual pipeline: strong form → weak form → discretization → element integrals → global system → solve.
  • One view: in practice, many users skip derivations and rely on textbook element formulations.
  • Recommendations for deeper understanding include finite difference methods as a starting point, university FEM courses, and coding with libraries like deal.II or FEniCS.

Debate on FEM’s Role in Design

  • One camp: FEM is best as a “unit test” or verification tool; rapid physical prototyping and iteration can be more effective, especially for mechanisms and tolerances.
  • Counterpoint: what works for exceptional engineers or small prototypes does not scale to large or safety-critical structures (bridges, large aerospace/automotive structures, crashworthiness).
  • Strong disagreement over claims like “you can’t design crash-resilient structures without FEM”:
    • Historical argument: major structures and vehicles were designed pre-FEM, so it’s not strictly necessary.
    • Modern argument: complexity and performance expectations now make high-fidelity simulation essential to meet requirements, reduce testing cost, and satisfy certification.

Limitations, Validation, and “Next-Gen” Methods

  • Experienced analysts emphasize that “garbage in, garbage out”: misunderstanding models or parameters leads to wildly wrong results; hand checks and fundamentals remain crucial.
  • Reports that many “next generation” FEM ideas work on simple benchmark problems but fail to validate on complex real-world cases; industry focus has shifted toward Verification & Validation standards (e.g., ASME V&V).
  • Physics-informed neural networks, neural operators, and ML-based solvers are being explored:
    • Early impressions: very fast and directionally correct, but not yet accurate enough for final design; may serve as pre-screening tools.

Isogeometric Analysis (IGA) and Meshing Pain Points

  • IGA (using spline-based CAD functions as shape functions) highlighted as a promising direction:
    • Claims of better accuracy per degree of freedom, larger stable timesteps, improved stability for problems like incompressible solids, and immersed/trimmed methods that greatly ease meshing.
  • Skeptical view: IGA’s core idea—reusing CAD splines for shape functions—has existed for years, with limited industrial impact and questionable benefit over classical p-refinement.
  • Proponents respond that modern spline technology, hierarchical refinement, and trimming-based immersed methods do offer real gains, particularly by reducing meshing effort while retaining good convergence.