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A-Priori Convergence Analysis of a Discontinuous Galerkin Time-Domain Method to Solve Maxwell’s Equations on Hybrid Meshes

In: Numerical Mathematics and Advanced Applications 2011

Author

Listed:
  • C. Durochat

    (INRIA Sophia Antipolis – Méditerranée research center 2004 Route des Lucioles, Nachos project-team)

  • C. Scheid

    (University of Nice – Sophia Antipolis, Jean-Alexandre Dieudonné Mathematics Laboratory)

Abstract

We study a multi-element Discontinuous Galerkin Time Domain (DGTD) method for solving the system of unsteady Maxwell equations. This method is formulated on a non-conforming and hybrid mesh combining a structured (orthogonal, large size elements) quadrangulation of the regular zones of the computational domain with an unstructured triangulation for the discretization of the irregularly shaped objects. The main objective is to enhance the flexibility and the efficiency of DGTD methods. Within each element, the electromagnetic field components are approximated by a high order nodal polynomial, using a centered flux for the surface integrals and a second order Leap-Frog scheme for the time integration of the associated semi-discrete equations. We formulate the 3D discretization scheme, present the results of mathematical analysis (L 2 stability and a-priori convergence in 3D). Finally, the 2D numerical performance and convergence is demonstrated.

Suggested Citation

  • C. Durochat & C. Scheid, 2013. "A-Priori Convergence Analysis of a Discontinuous Galerkin Time-Domain Method to Solve Maxwell’s Equations on Hybrid Meshes," Springer Books, in: Andrea Cangiani & Ruslan L. Davidchack & Emmanuil Georgoulis & Alexander N. Gorban & Jeremy Levesley (ed.), Numerical Mathematics and Advanced Applications 2011, edition 127, pages 91-99, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-33134-3_10
    DOI: 10.1007/978-3-642-33134-3_10
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