High order non-conforming multi-element discontinuous Galerkin method for time-domain electromagnetics
type: Dataset
description: This thesis is concerned with the study of a Discontinuous Galerkin Time-Domain method (DGTD), for the numerical resolution of the unsteady Maxwell equations on hybrid tetrahedral/hexahedral in 3D (triangular/quadrangular in 2D) and non-conforming meshes, denoted by DGTD-PpQk method. Like in several studies on various hybrid time domain methods (such as a combination of Finite Volume with Finite Difference methods, or Finite Element with Finite Difference, etc.), our general objective is to mesh objects with complex geometry by tetrahedra for high precision and mesh the surrounding space by square elements for simplicity and speed. In the discretization scheme of the DGTD method considered here, the electromagnetic field components are approximated by a high order nodal polynomial, using a centered approximation for the surface integrals. Time integration of the associated semi-discrete equations is achieved by a second or fourth order Leap-Frog scheme. After introducing the historical and physical context of Maxwell equations, we present the details of the DGTD-PpQk method. We prove the L2 stability of this method by establishing the conservation of a discrete analog of the eletromagnetic energy and a sufficient CFL-like stability condition is exhibited. The theoritical convergence of the scheme is also studied, this leads to a-priori error estimate that takes into account the hybrid nature of the mesh. Afterward, we perform a complete numerical study in 2D (TMz waves), for several test problems, on hybrid and non-conforming meshes, and for homogeneous or heterogeneous media. We do the same for the 3D implementation, with more realistic simulations, for example the propagation in a heterogeneous human head model. We show the consistency between the mathematical and numerical results of this DGTD-PpQk method, and its contribution in terms of accuracy and CPU time.
issued: 2026-05-11T22:29:16.623907
language: fr
modified: 2026-05-11T22:29:16.623912
contact point: Organization
  fn: CCSD
keyword: convergence
keyword: cpu-time
keyword: discontinuous-galerkin-method
keyword: equations-de-maxwell
keyword: high-order-accuracy
keyword: hybrid-method
keyword: infoeu-reposemanticsdoctoralthesis
keyword: maillage-non-conforme
keyword: mathmath-apmathematics-mathanalysis-of-pdes-mathap
keyword: mathmath-namathematics-mathnumerical-analysis-mathna
keyword: maxwell-equations
keyword: methode-de-type-galerkin-discontinu
keyword: methode-hybride
keyword: multi-element
keyword: multi-elements
keyword: nonconforming-mesh
keyword: precision-dordre-eleve
keyword: stabilite
keyword: stability
keyword: temps-de-calcul
keyword: theses
landing page: https://theses.hal.science/tel-00805935

High order non-conforming multi-element discontinuous Galerkin method for time-domain electromagnetics
type: Distribution
format: HTML
issued: 2026-05-11T22:29:16.728566
modified: 2026-05-11T22:29:16.587837
access URL: https://theses.hal.science/tel-00805935

test_moissonnage_selune
type: Agent