{
  "annotation_id": "328d9d39-dabe-4931-bc2f-d4955d6bed86",
  "date_created": "2026-02-17T05:53:15.443000Z",
  "date_modified": "2026-02-17T05:53:15.443000Z",
  "file_hash": "93ba145be3019eaa9a9ab761bd477e303db012c8227e75af3c4fae561caafa0b",
  "private": false,
  "record": {
    "abstract": "It is found that the wave functions of the Gross-Pitaevskii equation (GPE) often vary significantly in different spatial regions, with some components exhibiting sharp variations while others remain smooth. Solving the GPE on a single mesh, even with adaptive refinement, can lead to excessive computational costs due to the need to accommodate the most oscillatory solution. To address this issue, we present a multi-mesh adaptive finite element method for solving the GPE. To this end, we first convert it into a time-dependent equation through the imaginary time propagation method. Then the equation is discretized by the backward Euler method temporally and the multi-mesh adaptive finite element method spatially. The proposed method is compared with the single-mesh adaptive method through a series of numerical experiments, which demonstrate that the multi-mesh adaptive method can achieve the same numerical accuracy with less computational consumption.",
    "arxiv_id": "2601.08299",
    "authors": [
      "Mingzhe Li",
      "Yang Kuang",
      "Zhicheng Hu"
    ],
    "categories": [
      "math.NA",
      "cs.NA",
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "A multi-mesh adaptive finite element method for solving the Gross-Pitaevskii equation",
    "url": "https://arxiv.org/abs/2601.08299",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "641b2c30-7977-4662-a620-d6a74618632e",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}