{
  "id": "1606.07428",
  "version": "v1",
  "published": "2016-06-23T01:06:21.000Z",
  "updated": "2016-06-23T01:06:21.000Z",
  "title": "An integral equation formulation for rigid bodies in Stokes flow in three dimensions",
  "authors": [
    "Eduardo Corona",
    "Leslie Greengard",
    "Manas Rachh",
    "Shravan Veerapaneni"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "We present a new derivation of a boundary integral equation (BIE) for simulating the three-dimensional dynamics of arbitrarily-shaped rigid particles of genus zero immersed in a Stokes fluid, on which are prescribed forces and torques. Our method is based on a single-layer representation and leads to a simple second-kind integral equation. It avoids the use of auxiliary sources within each particle that play a role in some classical formulations. We use a spectrally accurate quadrature scheme to evaluate the corresponding layer potentials, so that only a small number of spatial discretization points per particle are required. The resulting discrete sums are computed in $\\mathcal{O}(n)$ time, where $n$ denotes the number of particles, using the fast multipole method (FMM). The particle positions and orientations are updated by a high-order time-stepping scheme. We illustrate the accuracy, conditioning and scaling of our solvers with several numerical examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-23T01:06:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "integral equation formulation",
      "stokes flow",
      "rigid bodies",
      "dimensions",
      "simple second-kind integral equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}