Eigenmodes of periodic orbits for 2D multiple scattering problems

This implementation accompanies the article "On the eigenmodes of periodic orbits for multiple scattering problems in 2D", D. Huybrechs and P. Opsomer, submitted. We compute and validate a Taylor approximation of the equilibrium phase of the density in ray tracing. We initially exploit symmetry in the case of two circular scatterers, but also provide an explicit algorithm for an arbitrary number of general 2D obstacles. The coefficients, as well as the time to compute them, are independent of the wavenumber and of the incident wave.

Coupling modes in two circles

This implementation accompanies the article "Coupling modes in high-frequency multiple scattering problems: the case of two circles", D. Huybrechs and P. Opsomer, In UKBIM 11, Conference proceedings
(2017), D. Chappell, Ed., pp. 99–108. For the case of two circular scatterers, we compute a Taylor approximation of the equilibrium phase of the density in ray tracing. This is also the eigenvector of a matrix representing a full cycle of reflections, and we validate our results. The Taylor coefficients can be computed independently of the wavenumber and incident wave and correspond to the distance to the periodic orbit via an infinite number of reflections at equal angles, where one substracts the distance between the circles at each reflection.