{
  "id": "1701.00215",
  "version": "v1",
  "published": "2017-01-01T07:37:18.000Z",
  "updated": "2017-01-01T07:37:18.000Z",
  "title": "Weight-adjusted discontinuous Galerkin methods: matrix-valued weights and elastic wave propagation in heterogeneous media",
  "authors": [
    "Jesse Chan"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "Weight-adjusted inner products are easily invertible approximations to weighted $L^2$ inner products. These approximations can be paired with a discontinuous Galerkin (DG) discretization to produce a time-domain method for wave propagation which is low storage, energy stable, and high order accurate for arbitrary heterogeneous media and curvilinear meshes. In this work, we extend weight-adjusted DG (WADG) methods to the case of matrix-valued weights, with the linear elastic wave equation as an application. We present a DG formulation of the symmetric form of the linear elastic wave equation, with upwind-like dissipation incorporated through simple penalty fluxes. A semi-discrete convergence analysis is given, and numerical results confirm the stability and high order accuracy of WADG for several problems in elastic wave propagation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-01T07:37:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "elastic wave propagation",
      "weight-adjusted discontinuous galerkin methods",
      "heterogeneous media",
      "matrix-valued weights",
      "linear elastic wave equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}