A hybrid Hermite-discontinuous Galerkin method for hyperbolic systems with application to Maxwell's equations

Authors:
Xi (Ronald) Chen;Daniel Appelö;Thomas Hagstrom
Affiliations:
College of Optical Sciences, Arizona Center for Mathematical Sciences (ACMS), University of Arizona, Tucson, AZ 85721, United States;Department of Mathematics and Statistics, University of New Mexico, 1 University of New Mexico, Albuquerque, NM 87131, United States;Department of Mathematics, Southern Methodist University, PO Box 750156, Dallas, TX 75275, United States
Venue:
Journal of Computational Physics
Year:
2014

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Abstract

A high order discretization strategy for solving hyperbolic initial-boundary value problems on hybrid structured-unstructured grids is proposed. The method leverages the capabilities of two distinct families of polynomial elements: discontinuous Galerkin discretizations which can be applied on elements of arbitrary shape, and Hermite discretizations which allow highly efficient implementations on staircased Cartesian grids. We demonstrate through numerical experiments in 1+1 and 2+1 dimensions that the hybridized method is stable and efficient.