{
  "annotation_id": "a07243da-a90d-4bc2-b8f0-eb9163ca0f9b",
  "date_created": "2026-03-02T18:01:21.296000Z",
  "date_modified": "2026-03-02T18:01:21.296000Z",
  "file_hash": "e80a66a7641d43f8a69957a1458223168bbe7e5289996e6cc0782c908acedc62",
  "private": false,
  "record": {
    "abstract": "The multigrid algorithm is a multilevel approach to accelerate the numerical\nsolution of discretized differential equations in physical problems involving\nlong-range interactions. Multiresolution analysis of wavelet theory provides an\nefficient representation of functions which exhibit localized bursts of short\nlength-scale behavior. Applications such as computing the electrostatic field\nin and around a molecule should benefit from both approaches. In this work, we\ndemonstrate how a novel interpolating wavelet transform, which in itself is the\nsynthesis of finite element analysis and wavelet theory, may be used as the\nmathematical bridge to connect the two approaches. The result is a specialized\nmultigrid algorithm which may be applied to problems expressed in wavelet\nbases. With this approach, interpolation and restriction operators and grids\nfor the multigrid algorithm are predetermined by an interpolating\nmultiresolution analysis. We will present the new method and contrast its\nefficiency with standard wavelet and multigrid approaches.",
    "arxiv_id": "physics/9806034",
    "authors": [
      "D. Yesilleten",
      "T. A. Arias"
    ],
    "categories": [
      "physics.comp-ph",
      "cond-mat"
    ],
    "title": "The Hopgrid algorithm: multilevel synthesis of multigrid and wavelet   theory",
    "url": "https://arxiv.org/abs/physics/9806034"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "d039a789-536e-4a1f-a884-23589d1c8e08",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}