Mathematical Methods for Computational Physics

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

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

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

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

Recommended prerequisites:

Concepts of structured programming

CCI

• Distribution theory, Green's functions.
• Sobolev spaces and trace spaces.
• Variational formulation of elliptic boundary value problems.
• Integral equations, singular integral operators, microlocal analysis.
• Introduction to finite element methods.
• Discrete dipole method and "Fast Multipole" method.