• 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.

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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.

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Necessary pre-requisites

Mathematics courses for physics (integration, Fourier analysis, complex analysis, linear algebra)

Recommended Prerequisites:

Concepts of structured programming

 

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Knowledge control

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".
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