Level of Education
5 years of post-secondary education
ECTS
3 credits
Training Structure
College of Sciences
Number of hours
21h
Description
Mathematics for Computational Physics. Introduction to 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 computational physics. Solve variational or integral equations using finite element methods. Solve diffraction problems using the discrete dipole method.
Mandatory Prerequisites
Math Courses for Physics (Integration, Fourier Analysis, Complex Analysis, Linear Algebra)
Recommended prerequisites:
Concepts of Structured Programming
Knowledge Assessment
CCI
Course Outline
- 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 the Finite Element Method.
- Discrete Dipole Method and "Fast Multipoles" Method.