Title: A boundary conformal discontinuous Galerkin approach for electro-quasistatic field problems on Cartesian grids

Authors: Annette Fröhlcke; Erion Gjonaj; Thomas Weiland

Addresses: Graduate School of Computational Engineering, Technische Universität Darmstadt, Dolivostr. 15, 64293 Darmstadt, Germany ' Computational Electromagnetics Laboratory, Technische Universität Darmstadt, Schloßgartenstr. 8, 64289 Darmstadt, Germany ' Computational Electromagnetics Laboratory, Technische Universität Darmstadt, Schloßgartenstr. 8, 64289 Darmstadt, Germany

Abstract: A boundary conformal approach for solving three-dimensional electro-quasistatic field problems with a high order discontinuous Galerkin method on Cartesian grids is proposed. The method is based on a novel cut-cell discretisation which is applied only on elements intersected by curved material boundaries. A particular numerical quadrature is introduced which allows for an accurate integration of the high order finite element operators taking into account the exact geometry of the cut-cells. Furthermore, a general hybridisation of the cut-cell approach with the conventional finite element method in the homogeneous parts of the computational domain is proposed. Numerical examples are presented which demonstrate the accuracy of this discretisation method for practical problems with curved geometries.

Keywords: boundary conformal discretisation; discontinuous Galerkin method; high order methods; FE-DG hybridisation; electro-quasistatic fields; Cartesian grids; cut-cell discretisation; finite element method; FEM; curved geometries.

DOI: 10.1504/IJCSE.2014.064533

International Journal of Computational Science and Engineering, 2014 Vol.9 No.5/6, pp.478 - 483

Received: 23 Dec 2011
Accepted: 21 Sep 2012

Published online: 22 Sep 2014 *

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