Simulation in electromagnetism

This unit deals with the solution of electromagnetic problems on a computer. From Maxwell's equations, it shows how to simulate the behavior of electromagnetic waves in different media. It includes a detailed implementation of simulations based on the Finite Difference Time Domain (FDTD) method.

An introduction to the problems of diffraction in the harmonic regime by a bounded obstacle will be given for the case of scalar waves in 2D and 3D.

Upon completion of this UE, students will be able to:

• Apply a finite-difference time-domain (FDTD) numerical scheme to discretize Maxwell's equations at 1D, 2D and 3D
• Implement the FDTD method in Python using the Numpy and Matplotlib libraries
• Simulate the propagation of electromagnetic waves in different media
• Choose the appropriate parameters to ensure the stability of the digital schema and limit the errors resulting from digital processing.
• Model a diffraction problem in the harmonic regime and know some modal methods.

M1 in Physics

Recommended Prerequisites:

Python programming

CCI

• Recall of Python, use of NumPy and Matplotlib libraries
• Treatment of the wave equation with the finite difference time domain (FDTD) method
• Simulation of the propagation of electromagnetic waves in different 1D media and analysis of the effect of the different parameters introduced in the numerical simulation.
• Yee's mesh
• Perfect Matching Layer (PML)
• Introduction to MATLAB Programming
• Theory of diffraction by a bounded obstacle in the harmonic regime (2d-3d) for scalar waves
• Implementation of a modal method in the case of a circular or spherical obstacle
• Introduction to the resonant structure of the diffraction matrix.