{
  "id": "1408.4495",
  "version": "v1",
  "published": "2014-08-19T22:44:16.000Z",
  "updated": "2014-08-19T22:44:16.000Z",
  "title": "Sparsifying Preconditioner for the Lippmann-Schwinger Equation",
  "authors": [
    "Lexing Ying"
  ],
  "comment": "18 pages",
  "categories": [
    "math.NA"
  ],
  "abstract": "The Lippmann-Schwinger equation is an integral equation formulation for acoustic and electromagnetic scattering from an inhomogeneous media and quantum scattering from a localized potential. We present the sparsifying preconditioner for accelerating the iterative solution of the Lippmann-Schwinger equation. This new preconditioner transforms numerically the discretized Lippmann-Schwinger equation into a sparse form and leverages the efficient sparse linear algebra algorithms for computing the approximate inverse. This preconditioner is efficient and easy to implement. When combined with standard iterative methods, it results almost frequency-independent iteration number. We provide 2D and 3D numerical results to demonstrate the effectiveness of this new preconditioner.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-19T22:44:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sparsifying preconditioner",
      "efficient sparse linear algebra algorithms",
      "integral equation formulation",
      "frequency-independent iteration number",
      "discretized lippmann-schwinger equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.4495Y"
    }
  }
}