convergence-study
Spatial and temporal convergence analysis with Richardson extrapolation and Grid Convergence Index (GCI) for solution verification
differentiation-schemes
Select and apply numerical differentiation schemes for PDE/ODE discretization. Use when choosing finite difference/volume/spectral schemes, building stencils, handling boundaries, estimating truncation error, or analyzing dispersion and dissipation.
linear-solvers
Select and configure linear solvers for systems Ax=b in dense and sparse problems. Use when choosing direct vs iterative methods, diagnosing convergence issues, estimating conditioning, selecting preconditioners, or debugging stagnation in GMRES/CG/BiCGSTAB.
mesh-generation
Plan and evaluate mesh generation for numerical simulations. Use when choosing grid resolution, checking aspect ratios/skewness, estimating mesh quality constraints, or planning adaptive mesh refinement for PDE discretization.
nonlinear-solvers
Select and configure nonlinear solvers for f(x)=0 or min F(x). Use for Newton methods, quasi-Newton (BFGS, L-BFGS), Broyden, Anderson acceleration, diagnosing convergence issues, choosing line search vs trust region, and analyzing Jacobian quality.
numerical-integration
Select and configure time integration methods for ODE/PDE simulations. Use when choosing explicit/implicit schemes, setting error tolerances, adapting time steps, diagnosing integration accuracy, planning IMEX splitting, or handling stiff/non-stiff coupled systems.
numerical-stability
Analyze and enforce numerical stability for time-dependent PDE simulations. Use when selecting time steps, choosing explicit/implicit schemes, diagnosing numerical blow-up, checking CFL/Fourier criteria, von Neumann analysis, matrix conditioning, or detecting stiffness in advection/diffusion/reaction problems.
time-stepping
Plan and control time-step policies for simulations. Use when coupling CFL/physics limits with adaptive stepping, ramping initial transients, scheduling outputs/checkpoints, or planning restart strategies for long runs.
slurm-job-script-generator
Generate SLURM `sbatch` job scripts and sanity-check HPC resource requests (nodes, tasks, CPUs, memory, GPUs) for simulation runs. Use when preparing submission scripts, deciding MPI vs MPI+OpenMP layouts, standardizing `#SBATCH` directives, or debugging job launch configuration (`sbatch`/`srun`).
ontology-explorer
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ontology-mapper
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ontology-validator
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parameter-optimization
Explore and optimize simulation parameters via design of experiments (DOE), sensitivity analysis, and optimizer selection. Use for calibration, uncertainty studies, parameter sweeps, LHS sampling, Sobol analysis, surrogate modeling, or Bayesian optimization setup.
performance-profiling
Identify computational bottlenecks, analyze scaling behavior, estimate memory requirements, and receive optimization recommendations for any computational simulation. Use when simulations are slow, investigating parallel efficiency, planning resource allocation, or seeking performance improvements through timing analysis, scaling studies, memory profiling, or bottleneck detection.
post-processing
Extract, analyze, and visualize simulation output data. Use for field extraction, time series analysis, line profiles, statistical summaries, derived quantity computation, result comparison to references, and automated report generation from simulation results.
simulation-orchestrator
Orchestrate multi-simulation campaigns including parameter sweeps, batch jobs, and result aggregation. Use for running parameter studies, managing simulation batches, tracking job status, combining results from multiple runs, or automating simulation workflows.
simulation-validator
Validate simulations before, during, and after execution. Use for pre-flight checks, runtime monitoring, post-run validation, diagnosing failed simulations, checking convergence, detecting NaN/Inf, or verifying mass/energy conservation.