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Algebraic multigrid techniques for discontinuous Galerkin methods with varying polynomial order |
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| Authors: | C Siefert R Tuminaro A Gerstenberger G Scovazzi S S Collis |
| Institution: | 1. Computational Shock and Multiphysics Department, Sandia National Laboratories, P.O. Box 5800, MS 1320, Albuquerque, NM, 87185-1320, USA 2. Numerical Analysis and Applications Department, Sandia National Laboratories, P.O. Box 5800, MS 1319, Albuquerque, NM, 87185-1319, USA 3. Department of Civil and Environmental Engineering, Duke University, Room 121 Hudson Hall, Box 90287, Durham, NC, 27708-0287, USA |
| Abstract: | We present a parallel algebraic multigrid (AMG) algorithm for the implicit solution of the Darcy problem discretized by the discontinuous Galerkin (DG) method that scales optimally for regular and irregular meshes. The main idea centers on recasting the preconditioning problem so that existing AMG solvers for nodal lower order finite elements can be leveraged. This is accomplished by a transformation operator which maps the solution from a Lagrange basis representation to a Legendre basis representation. While this mapping function must be user supplied, we demonstrate how easily it can be constructed for somepopular finite element representations includingquadrilateral/hexahedral and triangular/tetrahedral DG formulations. Furthermore, we show that the mapping does not depend on the Jacobian transformation between reference and physical space and so it can be constructed with very limited mesh information. Parallel performance studies demonstrate the versatility of this approach. |
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