{
  "id": "lib-process:mathematics--pde-solver-selection",
  "_kind": "LibraryProcess",
  "_file": "generated-library/processes.yaml",
  "_cluster": "generated-library",
  "attributes": {
    "displayName": "pde-solver-selection",
    "description": "Guide selection of appropriate numerical methods for partial differential equations\nbased on problem characteristics (elliptic, parabolic, hyperbolic), boundary conditions, and accuracy requirements.",
    "libraryPath": "library/specializations/domains/science/mathematics/pde-solver-selection.js",
    "specialization": "mathematics",
    "references": [
      "- LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations\n- Morton & Mayers, Numerical Solution of PDEs\n- Hughes, The Finite Element Method\n- Trefethen, Spectral Methods in MATLAB"
    ],
    "example": "const result = await orchestrate('specializations/domains/science/mathematics/pde-solver-selection', {\n  pdeDescription: 'Heat diffusion in 2D rectangular domain',\n  pdeEquation: 'u_t = alpha * (u_xx + u_yy)',\n  boundaryConditions: { type: 'Dirichlet', values: 'fixed temperature on all boundaries' },\n  domain: { shape: 'rectangle', dimensions: [1, 1] },\n  accuracyRequirements: { spatialOrder: 2, temporalOrder: 2, relativeTolerance: 1e-6 }\n});",
    "usesAgents": [
      "pde-expert",
      "numerical-analyst"
    ]
  },
  "outgoingEdges": [
    {
      "from": "lib-process:mathematics--pde-solver-selection",
      "to": "skill-area:statistical-analysis",
      "kind": "lib_requires_skill_area",
      "attributes": {
        "weight": 1
      }
    },
    {
      "from": "lib-process:mathematics--pde-solver-selection",
      "to": "skill-area:mathematical-reasoning",
      "kind": "lib_requires_skill_area",
      "attributes": {
        "weight": 0.7
      }
    },
    {
      "from": "lib-process:mathematics--pde-solver-selection",
      "to": "skill-area:data-analysis",
      "kind": "lib_requires_skill_area",
      "attributes": {
        "weight": 0.5
      }
    },
    {
      "from": "lib-process:mathematics--pde-solver-selection",
      "to": "domain:mathematics",
      "kind": "lib_applies_to_domain",
      "attributes": {
        "weight": 1
      }
    },
    {
      "from": "lib-process:mathematics--pde-solver-selection",
      "to": "role:research-engineer",
      "kind": "lib_involves_role",
      "attributes": {
        "weight": 1
      }
    },
    {
      "from": "lib-process:mathematics--pde-solver-selection",
      "to": "role:computational-scientist",
      "kind": "lib_involves_role",
      "attributes": {
        "weight": 0.7
      }
    },
    {
      "from": "lib-process:mathematics--pde-solver-selection",
      "to": "workflow:experiment-design",
      "kind": "lib_implements_workflow",
      "attributes": {
        "weight": 1
      }
    },
    {
      "from": "lib-process:mathematics--pde-solver-selection",
      "to": "specialization:computational-mathematics",
      "kind": "lib_belongs_to_specialization",
      "attributes": {
        "weight": 1
      }
    },
    {
      "from": "lib-process:mathematics--pde-solver-selection",
      "to": "specialization:mathematics",
      "kind": "lib_belongs_to_specialization",
      "attributes": {
        "weight": 0.9
      }
    },
    {
      "from": "lib-process:mathematics--pde-solver-selection",
      "to": "lib-agent:mathematics--pde-expert",
      "kind": "uses_agent",
      "attributes": {
        "weight": 0.8
      }
    },
    {
      "from": "lib-process:mathematics--pde-solver-selection",
      "to": "lib-agent:mathematics--numerical-analyst",
      "kind": "uses_agent",
      "attributes": {
        "weight": 0.8
      }
    }
  ],
  "incomingEdges": []
}