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 Mah

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.

Scholarships
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

Universit%C3%A9 de Rennes 1
Address: UFR de Math%C3%A9matiques, UFR Math%C3%A9matiques - Campus de Beaulieu 263 avenue du G%C3%A9n%C3%A9ral Leclerc - CS 74205
Postal code: 35042 Rennes Cedex FRANCE
City: Rennes
Country: France
Website: https://is2csa.univ-rennes1.fr/
E-mail: is2csa@univ-rennes1.fr
Phone: +33 (0)2 23 23 56 60