{
  "annotation_id": "5d04a96b-c8d4-43c7-a97a-5c3d32b45102",
  "date_created": "2026-03-02T18:00:43.262000Z",
  "date_modified": "2026-03-02T18:00:43.262000Z",
  "file_hash": "55fb4977be9e3e5e209973e2ad24f280a5fdde9354b30585b8742cb2f77565bf",
  "private": false,
  "record": {
    "abstract": "Three numerical algorithms are proposed to solve the time-dependent\nelastodynamic equations in elastic solids. All algorithms are based on\napproximating the solution of the equations, which can be written as a matrix\nexponential. By approximating the matrix exponential with a product formula, an\nunconditionally stable algorithm is derived that conserves the total elastic\nenergy density. By expanding the matrix exponential in Chebyshev polynomials\nfor a specific time instance, a so-called ``one-step\u0027\u0027 algorithm is constructed\nthat is very accurate with respect to the time integration. By formulating the\nconventional velocity-stress finite-difference time-domain algorithm (VS-FDTD)\nin matrix exponential form, the staggered-in-time nature can be removed by a\nsmall modification, and higher order in time algorithms can be easily derived.\nFor two different seismic events the accuracy of the algorithms is studied and\ncompared with the result obtained by using the conventional VS-FDTD algorithm.",
    "arxiv_id": "physics/0301050",
    "authors": [
      "J. S. Kole"
    ],
    "categories": [
      "physics.geo-ph",
      "physics.comp-ph"
    ],
    "title": "Solving seismic wave propagation in elastic media using the matrix   exponential approach",
    "url": "https://arxiv.org/abs/physics/0301050"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "7cacb83b-9ee8-4907-b6f9-97a9dbacc69b",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}