Level of study
BAC +5
ECTS
3 credits
Component
Faculty of Science
Hourly volume
21h
Description
Teaching of mathematics for numerical physics. Introduction of tools for the study of partial differential equations (distributions, variational formulation, Sobolev spaces).
Introduction to integral methods and their numerical implementation. Applications to diffraction problems in the harmonic regime.
Objectives
Provide fundamental mathematical tools for numerical physics. Solve variational or integral equations by finite element methods. Solve diffraction problems by the discrete dipole method.
Necessary pre-requisites
Mathematics courses for physics (integration, Fourier analysis, complex analysis, linear algebra)
Recommended Prerequisites:
Concepts of structured programming
Knowledge control
CCI
Syllabus
- Distribution theory, Green's functions.
- Sobolev spaces and trace spaces.
- Variational formulation of elliptic boundary problems.
- Integral equations, singular integral operators, microlocal analysis.
- Introduction to finite element methods.
- Method of discrete dipoles and "Fast Multipoles".