{
  "id": "2103.00726",
  "version": "v1",
  "published": "2021-03-01T03:23:34.000Z",
  "updated": "2021-03-01T03:23:34.000Z",
  "title": "Computation of transmission eigenvalues by the regularized Schur complement for the boundary integral operators",
  "authors": [
    "Yunyun Ma",
    "Fuming Ma",
    "Yukun Guo",
    "Jingzhi Li"
  ],
  "comment": "20 pages, 10 figures",
  "categories": [
    "math.NA",
    "cs.NA",
    "math.AP"
  ],
  "abstract": "This paper is devoted to the computation of transmission eigenvalues in the inverse acoustic scattering theory. This problem is first reformulated as a two by two boundary system of boundary integral equations. Next, utilizing the Schur complement technique, we develop a Schur complement operator with regularization to obtain a reduced system of boundary integral equations. The Nystr\\\"{o}m discretization is then used to obtain an eigenvalue problem for a matrix. We employ the recursive integral method for the numerical computation of the matrix eigenvalue. Numerical results show that the proposed method is efficient and reduces computational costs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-01T03:23:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "boundary integral operators",
      "regularized schur complement",
      "transmission eigenvalues",
      "boundary integral equations",
      "reduces computational costs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}