SPFCU45

UE Advanced computational EM methods

Unité d'enseignement (UE) de 3 crédits

^En UE enseignée en Anglais

DESCRIPTION
ORGANISATION
FORMATIONS

Contenu

Direct methods in computational EM with the finite element method (18 hours)

This lecture will contain a theoretical part and also numerical demonstrations realized by the teacher and training classes for the students using dedicated softwares : Gmsh/GetDP for the Finite Element Method

Finite Element Method and introduction to Gmsh/GetDP softwares
Basic principles with a one dimensional example
Few words on the Galerkin method and the boundary conditions
Domain discretization and interpolating functions
Numerical dispersion
Vector problem and edge elements
Eigenvalue problems in the harmonic regime (modal analysis): 1D and 2D scalar examples
From classical Maxwell equations to their weak formulation
Use of the mesh generator Gmsh and use of the solver GetDP : 3 simples examples
Survey of more advanced topics (if possible) : perfect matching layers, outgoing wave condition, periodicity, vector field and 3D case, operator point of view, symmetry properties in electrodynamics and their use in numerical modelling

Inverse methods for characterization and imaging (14 hours)

Compétences à acquérir

Understanding the theoretical basics of computational EM with the finite element method
Knowing of the basic methodology in the correct use of numerical modelling softwares
Know-how to use the open-source FEM softwares Gmsh and Getdp to solce simple EM problems

Langue(s) d'enseignement

Anglais

Bibliographie

J.-M. Jin , The finite element method in electromagnetics, 3rd edition, Wiley, 2014
M. G. Larson, and rengzon , The Finite Element Method: Theory, Implementation, and Practice", Springer, 2010
J.-M. Jin , Theory and computation of electromagnetic fields, Wiley, 2010

D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, Springer, 2019
X. Chen, Computational Methods for Electromagnetic Inverse Scattering, Wiley, 2018
P.M. van den Berg, Forward and Inverse Scattering Algorithms Based on Contrast Source Integral Equations, Wiley, 2021

Prérequis obligatoires

Basic knowledge in electrodynamics, guided optics, differential equations and integration in maths

Prérequis recommandés

Functional space analysis, Linear algebra

Modalités d'organisation

This course is a classical lecture with some excercises on computers for the finite element part.

Volume des enseignements

Cours magistraux: 22 heures
Travaux dirigés: 10 heures
Volume total: 32 heures

Responsables pédagogiques:

RENVERSEZ Gilles
LITMAN Amelie

Codes APOGÉE

SPFCU45J [ELP]