Contribution in solving Maxwell's equations in periodic structures by the finite element method
type: Dataset
description: Electromagnetic periodic structures are of great interest. These structures act as frequency filters and allow the manufacturing of meta-materials which appear to be composite and artificial. They exhibit electromagnetic properties that are unusual to natural materials such as band gaps. This allows new devices to guide, focus or stop the propagation. This is for example useful to avoid coupling between various radiating elements via the characterization of the surface waves which propagate at the interface between air and the periodic structure. This thesis provides a description of the finite element method dedicated to the characterization of periodic structures. Numerical modelling results in eigenvalue problems of large sizes. It involves solving linear systems compounds of sparse matrices. A method is therefore discussed for solving this type of problem, optimizing and combining different algorithms. Before discussing the different aspects of the developed method, we establish an exhaustive list of all the existing methods by stating their advantages and drawbacks. We note that the finite element method can handle a wide range of periodic structures in three dimensions without limitation on their shape. We present different formulations of this method. Then the algorithmic aspects of the method are detailed. We show that an analysis of the resolution settings can impact the physical interpretations of the results. Finally we show the performance of our tool on classical validation results from the bibliography and we discuss the characterization of surface waves. Therefore, the study of a patch antenna array included in metal cavities is conducted. To conclude we can say that the studies conducted in this thesis have resulted in the production of a code used in an environment calculation initially present at ONERA.
issued: 2026-05-09T03:07:53.074749
language: fr
modified: 2026-05-09T03:07:53.074754
contact point: Organization
  fn: CCSD
keyword: bande-interdite-electromagnetique
keyword: couplage-mutuel
keyword: eigenmode-solver
keyword: eigenvalue-problems
keyword: electromagnetic-band-gap
keyword: finite-element-method
keyword: infoeu-reposemanticsdoctoralthesis
keyword: infoinfo-mocomputer-science-csmodeling-and-simulation
keyword: mathmath-apmathematics-mathanalysis-of-pdes-mathap
keyword: matrices-creuses
keyword: methode-des-elements-finis
keyword: modes-de-surface
keyword: mutual-coupling
keyword: periodic-structures
keyword: problemes-aux-valeurs-propres
keyword: solveur-mode-propre
keyword: sparse-matrices
keyword: spielecengineering-sciences-physicselectromagnetism
keyword: structures-periodiques
keyword: surface-modes
keyword: theses
landing page: https://theses.hal.science/tel-00878558

Contribution in solving Maxwell's equations in periodic structures by the finite element method
type: Distribution
format: HTML
issued: 2026-05-09T03:07:53.084606
modified: 2026-05-09T03:07:53.049845
access URL: https://theses.hal.science/tel-00878558

test_moissonnage_selune
type: Agent