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High order non-conforming multi-element Discontinuous Galerkin method for time domain electromagnetics

Abstract : We study a high order Discontinuous Galerkin Time Domain (DGTD) method for solving the system of Maxwell equations. This method is formulated on a non-conforming multi-element mesh mixing an unstructured triangulation for the discretization of irregularly shaped objects with a structured (Cartesian) quadrangulation for the rest of the computational domain. Within each element, the electromagnetic field components are approximated by a high order nodal polynomial. The DG method proposed here makes use of a centered scheme for the definition of the numerical traces of the electric and magnetic fields at element interfaces, associated to a second order or fourth order leap-frog scheme for the time integration of the associated semi-discrete equations. We formulate this DGTD method in 3D and study its theoretical properties. In particular, an a priori convergence estimation is elaborated. Finally, we present numerical results for the application of the method to 2D test problems.
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Contributor : Stéphane Lanteri Connect in order to contact the contributor
Submitted on : Thursday, March 7, 2013 - 4:24:02 PM
Last modification on : Tuesday, October 25, 2022 - 4:17:30 PM
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Clement Durochat, Stéphane Lanteri, Claire Scheid. High order non-conforming multi-element Discontinuous Galerkin method for time domain electromagnetics. Applied Mathematics and Computation, 2013, 224, pp.681-704. ⟨10.1016/j.amc.2013.08.069⟩. ⟨hal-00797973⟩



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