Developments and challenges for the numerical analysis of time- modulated metamaterials (Jörg Nick)

18.11.2025 14:00 – 15:00

Time-modulated metamaterials have emerged as a focal point in the pursuit of next-generation materials. The talk discusses numerical investigation of acoustic
wave propagation in obstacles with periodically time-modulated material parameters. The first part of the talk discusses the numerical construction of Floquet–Bloch solutions, which are quasi-periodic kernel elements of the hyperbolic operator appearing on the left-hand side of the acoustic wave equation. Using the temporal Fourier expansion yields a system of coupled harmonics, which can be truncated. Instead, or in addition, we employ a general Galerkin space discretization to discretize in space. Some basic properties of the fully discretized modes can be shown and the convergence to the space or time-discretization can be established.

Complications in the theory, however, limit the connection to the fully continuous modulated wave equation when formulated as an initial value problem. A modification of the Floquet–Bloch approach yields modulated Fourier expansion for fast-time modulated media. For modulations with small amplitude, the solution of the time-modulated acoustic wave equation can be characterized by several slowly varying coefficient functions. As a consequence, we can derive fully discrete schemes that converge, under assumptions on the modulation, independently of the rapid oscillation of the physical parameters. Numerical experiments illustrate both approaches.

Lieu

Conseil Général 7-9, Room 1-05, Séminaire d'analyse numérique

entrée libre