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An Adaptive MFD Method for the Obstacle Problem Read chapter Read first chapter

2013 | OriginalPaper | Chapter

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

Authors : C. Durochat, C. Scheid

Published in: Numerical Mathematics and Advanced Applications 2011

Publisher: Springer Berlin Heidelberg

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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.

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previous chapter Moment-Based Boundary Conditions for Lattice Boltzmann Magnetohydrodynamics
next chapter Stabilization of a Degenerate Minimization Problem with the Single-Layer Potential
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Metadata
Title
A-Priori Convergence Analysis of a Discontinuous Galerkin Time-Domain Method to Solve Maxwell’s Equations on Hybrid Meshes
Authors
C. Durochat
C. Scheid
Copyright Year
2013
Publisher
Springer Berlin Heidelberg
Book
Numerical Mathematics and Advanced Applications 2011

Print ISBN: 978-3-642-33133-6

Electronic ISBN: 978-3-642-33134-3

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-3-642-33134-3_10

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