Mathematical Methods for Computational Physics

Teaching mathematics for numerical physics. Introduction of tools for studying partial differential equations (distributions, variational formulation, Sobolev spaces).

Introduction to integral methods and their numerical implementation. Applications to diffraction problems in the harmonic regime.

Provide fundamental mathematical tools for numerical physics. Solve variational or integral equations using finite element methods. Solve diffraction problems using the discrete dipole method.

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

Recommended prerequisites :

Notions of structured programming

CCI

• 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.
• Discrete dipole method and Fast Multipoles.