{
  "annotation_id": "ff7a5814-3e60-493b-87bf-5e35e90b6d81",
  "date_created": "2026-03-02T18:00:53.816000Z",
  "date_modified": "2026-03-02T18:00:53.816000Z",
  "file_hash": "786d87a1d8f33d840a5e812477081396462b240fef7de82370625a23dbe02d63",
  "private": false,
  "record": {
    "abstract": "An important class of problems exhibits smooth behaviour on macroscopic space\nand time scales, while only a microscopic evolution law is known. For such\ntime-dependent multi-scale problems, an \"equation-free\" framework has been\nproposed, of which patch dynamics is an essential component. Patch dynamics is\ndesigned to perform numerical simulations of an unavailable macroscopic\nequation on macroscopic time and length scales; it uses appropriately\ninitialized simulations of the available microscopic model in a number of small\nboxes (patches), which cover only a fraction of the space-time domain. To\nreduce the effect of the artificially introduced box boundaries, we use buffer\nregions to \"shield\" the boundary artefacts from the interior of the domain for\nshort time intervals. We analyze the accuracy of this scheme for a diffusion\nhomogenization problem with periodic heterogeneity, and propose a simple\nheuristic to determine a sufficient buffer size. The algorithm performance is\nillustrated through a set of numerical examples, which include a non-linear\nreaction-diffusion equation and the Kuramoto--Sivashinsky equation.",
    "arxiv_id": "physics/0412005",
    "authors": [
      "Giovanni Samaey",
      "Ioannis G. Kevrekidis",
      "Dirk Roose"
    ],
    "categories": [
      "physics.comp-ph"
    ],
    "title": "Patch dynamics with buffers for homogenization problems",
    "url": "https://arxiv.org/abs/physics/0412005"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "3de879ae-60db-4b36-8627-27edc2a35f86",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}