France, Rennes

Introduction to the Finite Element Method in optics

when 6 July 2015 - 17 July 2015
duration 2 weeks
credits 3 ECTS
fee EUR 600

Very frequently, equations in physics are too complicated to find solutions in closed form or by purely analytical means (e.g. by Laplace and Fourier transform methods, or in the form of a power series). Numerical approximations to the unknown analytical solution are therefore necessary.

The Finite Element Method (FEM) represents a powerful and general method for the approximate solution of partial differential equations. Although more complex to formulate and to implement than the popular Finite Difference Method (FDM), the FEM offers several important advantages such as the possibility of accurately following material interfaces, of imposing boundary continuity requirements for the approximated electromagnetic vector fields, etc.

The following topics will be covered:
Variational (weak) formulation of Partial Differential Equation (PDE) problems
Lagrange Finite element space
Finite element discretization of elliptic PDE
Edge/Vector Finite Elements for Maxwell equations

Course leader

Fabrice Mahé

Target group

Master level students in mathematics or physics. Students from third year undergraduate as well as PhD students are also be welcome.

Course aim

The aim of this course is to provide an introduction to both the mathematical theory and the numerical implementation of the FEM, with a special emphasis on applications in optics. Lectures will alternate with practical exercises using FEM software packages such as COMSOL Multi-Physics or Freefem++ and project work in groups of 3 or 4 students.

Fee info

EUR 600: Package A for students coming from partner universities.
This package includes:
Single room student accommodation within walking distance from the teaching building
Bedding and bath towels
Internet access
Access to common rooms
Coffee breaks, lunch and dinner
Bus tickets
Social activities
EUR 950: Package B for students coming from other universities or institutions.


2 grants covering part of the registration fees will be offered to foreign students with difficulties in financing their participation. A priority will be given to Master level students.Applications will be examined in 2 stages on March the 25th and April