From grimoire
Designs rigorous numerical simulations with formal V&V: defines mathematical models, selects methods (Monte Carlo, FDM, FEM), specifies convergence criteria, and quantifies uncertainty.
How this skill is triggered — by the user, by Claude, or both
Slash command
/grimoire:design-numerical-simulationThe summary Claude sees in its skill listing — used to decide when to auto-load this skill
Design a rigorous numerical simulation by defining the mathematical model, selecting the discretization or sampling method, specifying convergence criteria, quantifying uncertainty through sensitivity analysis, and validating results against analytical benchmarks or experimental data.
Design a rigorous numerical simulation by defining the mathematical model, selecting the discretization or sampling method, specifying convergence criteria, quantifying uncertainty through sensitivity analysis, and validating results against analytical benchmarks or experimental data.
Adopted by: NASA, DOE national laboratories, ESA, and every major engineering company use formal Verification and Validation (V&V) frameworks for numerical simulations. ASME V&V 10 (structural mechanics), V&V 20 (fluid mechanics), and AIAA G-077A (aeronautics) are the authoritative standards. The FDA's "Assessing the Credibility of Computational Modeling and Simulation" (2023) requires V&V for medical device simulations. Impact: Oberkampf & Roy (2010) demonstrate that simulation errors can be classified as verification errors (solving the equations wrong) vs. validation errors (solving the wrong equations) — a distinction that is critical for corrective action. The Space Shuttle Challenger and Columbia accidents were partly attributable to computational model failures that were not adequately validated. Quantifying simulation uncertainty (via sensitivity analysis and uncertainty propagation) is what separates credible simulations from false-precision tools.
Before writing any code:
Separation of concerns: the mathematical model (what physics/system you're modeling) is distinct from the numerical method (how you solve it). Keep both explicit.
Match method to problem type:
For spatial/temporal discretization:
f_exact ≈ f_fine + (f_fine − f_medium) / (r^p − 1)
where r = mesh refinement ratio, p = formal order of accuracy
For Monte Carlo:
Verification = "solving the equations correctly"
Distinguish two types:
Sensitivity analysis methods:
Sobol first-order index Sᵢ: fraction of output variance attributable to parameter i. Sobol total index Tᵢ: includes all interactions involving parameter i.
Validation = "solving the right equations"
npx claudepluginhub jeffreytse/grimoire --plugin grimoireDesigns and executes Monte Carlo simulations to evaluate finite-sample properties of statistical estimators including bias, RMSE, coverage, size, and power.
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