Janosch Preuss from University College London is visiting Makutu from May 20th to 25th. He will give the following seminar:
A hybridized Nitsche method for acoustic metamaterials
abstract: Acoustic metamaterials have some seemingly magical properties. For example, they can be used to render objects invisible to incoming sound waves (referred to as cloaking). At the PDE level these problems are characterized by a sign-change in the principal part of the operator across an interface. This renders their numerical treatment extremely challenging. To cope with this problem, we propose a primal dual stabilized FEM in which an interface variable is introduced to enforce the appropriate zero-jump conditions. We prove optimal convergence rates on arbitrary shape regular meshes (fitted to material interfaces) under a well-posedness assumption on the continuous problem. As numerical illustration we apply the method to simulate a cloaking device which has recently been proposed in the physics literature. In the second part of the talk we briefly discuss how the assumption that the mesh is fitted to the interface could be removed using the technology of unfitted isoparametric FEM. We applied these techniques recently to an ill-posed time-harmonic interface problem and analyzed the influence of the geometry approximation on the ability to reconstruct the wave from partial measurements. These studies are relevant for applications as the prospect of using simple background meshes to simulate wave propagation in complex geometries is very appealing.</p>
The talk is based on joint works with Erik Burman and Alexandre Ern.
