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The subject of this paper is multigrid solvers for Helmholtz operators with large wave numbers. Algorithms presented here are variations of the wave-ray solver which is modified to allow efficient solutions for operators with constant,…
We investigate TE-wave propagation in a hollow waveguide with a graded dielectric layer, described using a hyperbolic tangent function. General formulae for the electric field components of the TE-waves, applicable to hollow waveguides with…
We survey functional analytic methods for studying subwavelength resonator systems. In particular, rigorous discrete approximations of Helmholtz scattering problems are derived in an asymptotic subwavelength regime. This is achieved by…
The accurate calculation of guided electromagnetic modes in optical nanofibres is critical for applications in nanophotonics, from quantum interfaces to vectorial light sensing. Standard textbook methods rely on solving a $4\times4$ matrix…
We experimentally realized wide-mode-area slow-light modes in valley photonic crystals (VPhCs) heterostructure waveguides. The waveguides are fabricated on a silicon slab by inserting gapless photonic graphene layers with varying widths and…
We design compact waveguide couplers via impedance-tunable transformation optics. By tuning impedance coefficients in the original space, two-dimensional metallic and dielectric waveguide couplers are designed with a high efficiency.…
Superpositions of plane waves are known to approximate well the solutions of the Helmholtz equation. Their use in discretizations is typical of Trefftz methods for Helmholtz problems, aiming to achieve high accuracy with a small number of…
Solution of Helmholtz equation with impedance boundary condition on finite interval is equivalently reformulated as steady state of initial boundary value problem for first order hyperbolic system of partial differential equations.…
Closed combustion devices like gas turbines and rockets are prone to thermoacoustic instabilities. Design engineers in the industry need tools to accurately identify and remove instabilities early in the design cycle. Many different…
We present a numerical approach to efficiently calculate spin-wave dispersions and spatial mode profiles in magnetic waveguides of arbitrarily shaped cross section with any non-collinear equilibrium magnetization which is translationally…
The purpose of this research is to describe an efficient iterative method suitable for obtaining high accuracy solutions to high frequency time-harmonic scattering problems. The method allows for both refinement of local polynomial degree…
Due to its highly oscillating solution, the Helmholtz equation is numerically challenging to solve. To obtain a reasonable solution, a mesh size that is much smaller than the reciprocal of the wavenumber is typically required (known as the…
In this study we explore the possibility of simplifying the modeling of magnetohydrodynamic (MHD) slow body modes observed in photospheric magnetic structure such as the umbrae of sunspots and pores. The simplifying approach assumes that…
A method of higher-order modes filtering in an air-filled waveguide using a resistive layer is proposed. An analogue of Cremer's criterion is discussed and used to obtain the optimal modal attenuation of the non-planar waves while the plane…
We propose an iterative solution method for the 3D high-frequency Helmholtz equation that exploits a contour integral formulation of spectral projectors. In this framework, the solution in certain invariant subspaces is approximated by…
The Helmholtz equation is related to seismic exploration, sonar, antennas, and medical imaging applications. It is one of the most challenging problems to solve in terms of accuracy and convergence due to the scalability issues of the…
Waveguides are fundamental components in communication systems. However, they suffer from reflection and scattering losses at sharp routes or defects. The breakthrough in developing topological photonic crystals (PhCs) provides promising…
This paper deals with bathymetry-oriented optimization in the case of long waves with small amplitude. Under these two assumptions, the free-surface incompressible Navier-Stokes system can be written as a wave equation where the bathymetry…
Novel hollow-core THz waveguides featuring hyperuniform disordered reflectors are proposed, fabricated, and characterized. The reflector comprise aperiodically positioned dielectric cylinders connected with dielectric bridges. The proposed…
We consider the application of the WaveHoltz iteration to time-harmonic elastic wave equations with energy conserving boundary conditions. The original WaveHoltz iteration for acoustic Helmholtz problems is a fixed-point iteration that…