differentiation-schemes

Skills are folders of instructions, scripts, and resources that agents can

discover and use. Write once, use everywhere.

Each skill includes:

• SKILL.md with YAML frontmatter (name + description) and instructions
• scripts/ for deterministic workflows
• references/ for domain details loaded on demand

The agent discovers skills by name/description and loads the SKILL.md only

when the skill triggers. Scripts are executed directly for reliability.

Core Numerical Skills (`skills/core-numerical/`)

| Skill | Description |

|-------|-------------|

| numerical-stability | CFL analysis, von Neumann stability, stiffness detection |

| numerical-integration | Integrator selection, error norms, adaptive stepping |

| linear-solvers | Solver selection, preconditioner advice, convergence diagnostics |

| nonlinear-solvers | Newton/quasi-Newton selection, convergence diagnostics, globalization strategies |

| time-stepping | Time step planning, output scheduling, checkpointing |

| differentiation-schemes | Scheme selection, stencil generation, truncation error |

| mesh-generation | Grid sizing, mesh quality metrics |

Simulation Workflow Skills (`skills/simulation-workflow/`)

| Skill | Description |

|-------|-------------|

| simulation-validator | Pre-flight checks, runtime monitoring, post-flight validation |

| parameter-optimization | DOE sampling, optimizer selection, sensitivity analysis |

| simulation-orchestrator | Parameter sweeps, campaign management, result aggregation |

| post-processing | Field extraction, time series analysis, statistics, derived quantities |

| performance-profiling | Timing analysis, scaling studies, memory profiling, bottleneck detection |

Additional Resources

• Examples for each skill in examples/
• Comprehensive unit and integration tests in tests/
• CI/CD pipeline for cross-platform testing (Python 3.10-3.12)

1. Mention the skill by name in your request, or ask a task that matches its

description.

1. Run the scripts directly for reproducible outputs.
2. Optionally install skills into your agent's global skills directory for

reuse across projects.

Example:

```text

Use numerical-stability to check a proposed dt for my phase-field run.

```

This repo follows the Agent Skills standard, originating with [Anthropic](https://anthropic.com),

and is designed to work with Claude Code, Codex-style agents, and any tool that

supports SKILL.md-based skills.

Run the full test suite:

```bash

python3 -m unittest discover -s tests

```

Browse and run examples:

```bash

cat examples/README.md

```

```

skills/ # Skill packages (SKILL.md, scripts, references)

examples/ # Runnable CLI examples

tests/ # Unit + integration tests

```

• Agent Skills standard: https://agentskills.io
• Reference implementation: https://github.com/agentskills/agentskills