Abstract
A boundary conformal technique for solving three dimensional electro-quasistatic problems with a high order Discontinuous Galerkin method on Cartesian grids is proposed. The method is based on a cut-cell approach which is applied only on elements intersected by curved material boundaries. A particular numerical quadrature technique is applied which allows for an accurate integration of the finite element operators taking into account the exact geometry of the cut-cells. Two numerical examples are presented which demonstrate the optimal convergence rate of the method for arbitrary geometry.
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Thoma, P.: Zur numerischen Lösung der Maxwellschen Gleichungen im Zeitbereich. PhD Dissertation, TU Darmstadt (1997)
Dey, S., Mittra, R.: A locally conformal finite-difference time-domain (FDTD) algorithm modeling modeling three-dimensional perfectly conducting objects IEEE Microw. Guid. Wave Lett. 7, 273–275 (1997)
Arnold, D.N., Brezzi, F., Cockburn, B., Marini, D.: Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 39, 1749–1779 (2002)
Schöberl, J., Zaglmayr, S.: High order Nedelec elements with local complete sequence properties. COMPEL 24, 374–384 (2005)
OpenCascade 4.0, Open-Source Toolkit for 3D modeling (2001). URL: http://www.opencascade.com
Scholler, C., et al.: Numerical simulation of thermally coupled electromagnetic fields and fluid flow. In: Proceedings of Computational Methods for Coupled Problems in Science and Engineering, Papadrakakis, M., Onate, E., Schreffler, B. (eds.) CIMNE, Barcelona (2005), Santorini, Greece, May 2005
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© 2012 Springer-Verlag Berlin Heidelberg
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Fröhlcke, A., Gjonaj, E., Weiland, T. (2012). A Boundary Conformal DG Approach for Electro-Quasistatics Problems. In: Michielsen, B., Poirier, JR. (eds) Scientific Computing in Electrical Engineering SCEE 2010. Mathematics in Industry(), vol 16. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22453-9_17
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DOI: https://doi.org/10.1007/978-3-642-22453-9_17
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Online ISBN: 978-3-642-22453-9
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