{
  "id": "math/0408209",
  "version": "v1",
  "published": "2004-08-16T16:26:40.000Z",
  "updated": "2004-08-16T16:26:40.000Z",
  "title": "Optimization methods in direct and inverse scattering",
  "authors": [
    "Alexander G. Ramm",
    "Semion Gutman"
  ],
  "comment": "52 pages, 8 figures",
  "categories": [
    "math.NA",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In many Direct and Inverse Scattering problems one has to use a parameter-fitting procedure, because analytical inversion procedures are often not available. In this paper a variety of such methods is presented with a discussion of theoretical and computational issues. The problem of finding small subsurface inclusions from surface scattering data is solved by the Hybrid Stochastic-Deterministic minimization algorithm. A similar approach is used to determine layers in a particle from the scattering data. The Inverse potential scattering problem for spherically symmetric potentials and fixed-energy phase shifts as the scattering data is described. It is solved by the Stability Index Method. This general approach estimates the size of the minimizing sets, and gives a practically useful stopping criterion for global minimization algorithms. The 3D inverse scattering problem with fixed-energy data and its solution by the Ramm's method are discussed. An Obstacle Direct Scattering problem is treated by a Modified Rayleigh Conjecture (MRC) method. A special minimization procedure allows one to inexpensively compute scattered fields for 2D and 3D obstacles having smooth as well as nonsmooth surfaces. A new Support Function Method (SFM) is used for Inverse Obstacle Scattering problems. Another method for Inverse scattering problems, the Linear Sampling Method (LSM), is analyzed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-08-16T16:26:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "78A46",
      "65N21",
      "35R30"
    ],
    "keywords": [
      "optimization methods",
      "scattering data",
      "hybrid stochastic-deterministic minimization algorithm",
      "inverse obstacle scattering problems",
      "fixed-energy phase shifts"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 52,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......8209R"
    }
  }
}