{
  "id": "1608.01944",
  "version": "v1",
  "published": "2016-08-05T17:22:28.000Z",
  "updated": "2016-08-05T17:22:28.000Z",
  "title": "Weight-adjusted discontinuous Galerkin methods: wave propagation in heterogeneous media",
  "authors": [
    "Jesse Chan",
    "Russell J. Hewett",
    "T. Warburton"
  ],
  "comment": "Submitted to SISC",
  "categories": [
    "math.NA"
  ],
  "abstract": "Time-domain discontinuous Galerkin (DG) methods for wave propagation require accounting for the inversion of dense elemental mass matrices, where each mass matrix is computed with respect to a parameter-weighted L2 inner product. In applications where the wavespeed varies spatially at a sub-element scale, these matrices are distinct over each element, necessitating additional storage. In this work, we propose a weight-adjusted DG (WADG) method which reduces storage costs by replacing the weighted L2 inner product with a weight-adjusted inner product. This equivalent inner product results in an energy stable method, but does not increase storage costs for locally varying weights. A-priori error estimates are derived, and numerical examples are given illustrating the application of this method to the acoustic wave equation with heterogeneous wavespeed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-05T17:22:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "weight-adjusted discontinuous galerkin methods",
      "wave propagation",
      "heterogeneous media",
      "l2 inner product",
      "mass matrix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}