{
  "annotation_id": "f7f5ab83-a0f1-40d7-9461-1fe21db07ce3",
  "date_created": "2026-03-02T18:00:56.922000Z",
  "date_modified": "2026-03-02T18:00:56.922000Z",
  "file_hash": "89d62e088d5972b4311dd27b080535a581589c89a9afff8b8864f909a42692e4",
  "private": false,
  "record": {
    "abstract": "Based on a geometric discretization scheme for Maxwell equations, we unveil a\nmathematical\\textit{\\}transformation between the electric field intensity $E$\nand the magnetic field intensity $H$, denoted as Galerkin duality. Using\nGalerkin duality and discrete Hodge operators, we construct two system\nmatrices, $[ X_{E}] $ (primal formulation) and $[ X_{H} % ] $ (dual\nformulation) respectively, that discretize the second-order vector wave\nequations. We show that the primal formulation recovers the conventional\n(edge-element) finite element method (FEM) and suggests a geometric foundation\nfor it. On the other hand, the dual formulation suggests a new (dual) type of\nFEM. Although both formulations give identical dynamical physical solutions,\nthe dimensions of the null spaces are different.",
    "arxiv_id": "physics/0503013",
    "authors": [
      "Bo He",
      "F. L. Teixeira"
    ],
    "categories": [
      "physics.comp-ph",
      "physics.class-ph"
    ],
    "doi": "10.1016/j.physleta.2005.09.002",
    "title": "Geometric Finite Element Discretization of Maxwell Equations in Primal   and Dual Spaces",
    "url": "https://arxiv.org/abs/physics/0503013"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "54998b9f-0f45-4e9b-9995-f15791ad8149",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}