Electromagnetic waves impinging on three-dimensional helical metallic metamaterials have been shown to exhibit chiral effects of large magnitude both theoretically and in experimental realizations. Chirality here describes different responses of scatterers, materials, or metamaterials to left and right circularly polarized electromagnetic waves. These differences can be quantified in terms of novel chirality measures, which attain their minimal value zero for achiral scatterers, materials, or metamaterials that interact similarly with left and right circularly polarized waves. Scatterers, materials, or metamaterials with positive em-chirality measure show weaker interactions with either left or right circularly polarized waves, and maximally em-chiral scattering objects or media do not interact with fields of either positive or negative helicity at all.

In this talk we discuss the optimal design of thin metallic free-form nanowires that possess measures of electromagnetic chirality as large as fundamentally possible. We focus on optical frequencies and develop a gradient based optimization scheme to determine the optimal shape of highly chiral silver and gold nanowires. We discuss a series of numerical examples showing that the electromagnetic chirality measures of our optimized nanowires exceed those of traditional metallic helices. Therefore, these should be well suited as building blocks of novel metamaterials with an increased chiral response.

This is based on joint work with Ivan Fernandez-Corbaton (KIT), Marvin Knöller (University of Helsinki), and Carsten Rockstuhl (KIT). 

Pressure-robustness for fluid flow with inhomogeneous boundary conditions :

Using the Scott-Vogelius (SV) finite element for solving the Stokes equations yields exactly divergence free velocity approximations and therefore a pressure-robust method, i.e., the velocity error estimates are independent of the pressure. A key tool to obtain quasi-optimal velocity estimates is a stable, divergence-preserving Fortin operator that additionally satisfies certain trace preserving properties. We show such estimates for the SV method and an Iterated Penalty method approximating the discrete SV solutions for the Stokes problem subject to inhomogeneous boundary conditions. 

Dr. Karzan A. Berdawood (Salahaddin University-Erbil, Iraq / Goethe University Frankfurt) :

An Efficient Relaxed Alternating Algorithm for the Cauchy Problem Connected with the Helmholtz Equation 

The talk deals with alternating iterative methods for solving inverse Cauchy problems for the Helmholtz equation. The objective of restoring convergence, especially in challenging cases with large wave numbers (k) and of recovering lacking data on a part of the boundary based on the Cauchy data on the other part with accuracy. To overcome the instability, convergence and its slowness of the classical alternating iterative algorithm, two efficient relaxation techniques are proposed: one using a fixed relaxation parameter and the other using a dynamic parameter that is updated at each iteration. Both techniques enhance the robustness and convergence of the method without prior tuning. Theoretical results and numerical experiments demonstrate the stability, efficiency, and effectiveness of the proposed algorithms for this kind of ill-posed boundary value problem.

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