An elliptical lens

This variant of the video shows a linear wave reaching an elliptical area in which the speed of propagation is reduced to 75% of its value outside, which corresponds to an index of refraction of 4/3, as for water. Though the boundary of real lenses is usually made of the 3d equivalent of circular arcs, rather than elliptical ones, one can observe a similar focusing effect here. The colors show the energy density of the wave (obtained by adding squares of the time-derivative of the wave height, and the wave speed times the norm of their spatial gradient). There are absorbing boundary conditions on the sides of the domain, which however don’t work perfectly, which is why you see some waves reflected from the boundary. Music: “Glacial Melting Point“ by Asher Fulero@AsherFulero See also for more explanations (in French) on a few previous simulations of wave equations. The simulation solves the wave equation by discretization. The algorithm is adapted from the paper C code: Many thanks to my colleague Marco Mancini for helping me to accelerate my code!