{
  "annotation_id": "c14f40c3-592f-4fa1-9a07-7e1cf736d3e0",
  "date_created": "2026-03-02T18:01:21.748000Z",
  "date_modified": "2026-03-02T18:01:21.748000Z",
  "file_hash": "b21006b3d664cedad5152d626ec5d84e93f4a30a4d67073cb4db36e1dcc12ade",
  "private": false,
  "record": {
    "abstract": "Wavelets are a powerful new mathematical tool which offers the possibility to\ntreat in a natural way quantities characterized by several length scales. In\nthis article we will show how wavelets can be used to solve partial\ndifferential equations which exhibit widely varying length scales and which are\ntherefore hardly accessible by other numerical methods. As a benchmark\ncalculation we solve Poisson\u0027s equation for a 3-dimensional Uranium dimer. The\nlength scales of the charge distribution vary by 4 orders of magnitude in this\ncase. Using lifted interpolating wavelets the number of iterations is\nindependent of the maximal resolution and the computational effort therefore\nscales strictly linearly with respect to the size of the system.",
    "arxiv_id": "physics/9803011",
    "authors": [
      "Stefan Goedecker",
      "Oleg Ivanov"
    ],
    "categories": [
      "physics.comp-ph"
    ],
    "doi": "10.1063/1.168739",
    "title": "The solution of multi-scale partial differential equations using   wavelets",
    "url": "https://arxiv.org/abs/physics/9803011"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "afa02b70-223c-4b4a-bc73-e669e89c9e31",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}