A sharp relative-error bound for the Helmholtz h-FEM at high frequency

For the h-finite-element method (h-FEM) applied to the Helmholtz equation, the question of how quickly the meshwidth h must decrease with the frequency k to maintain accuracy as k increases has been studied since the mid 80’s. Nevertheless, there still do not exist in the literature any k-explicit bounds on the relative error of the FEM solution (the measure of the FEM error most often used in practical applications), apart from in one dimension. The main result of this paper is the sharp result that, for the lowest fixed-order conforming FEM (with polynomial degree, p, equal to one), the condition “$$h^2 k^3$$ h 2 k 3 sufficiently small" is sufficient for the relative error of the FEM solution in 2 or 3 dimensions to be controllably small (independent of k) for scattering of a plane wave by a nontrapping obstacle and/or a nontrapping inhomogeneous medium. We also prove relative-error bounds on the FEM solution for arbitrary fixed-order methods applied to scattering by a nontrapping obstacle, but these bounds are not sharp for $$p\ge 2$$ p ≥ 2 . A key ingredient in our proofs is a result describing the oscillatory behaviour of the solution of the plane-wave scattering problem, which we prove using semiclassical defect measures.

Application of cylindrical IE-GSTC to physical metasurfaces

<div>This work validates cylindrical IE-GSTC by applying it to physical metasurfaces, i.e. metasurfaces defined by material properties and dimensions rather than by susceptibility tensor components. Previously reported IE-GSTC which was formulated for zero thickness GSTC discontinuity is extended to handle finite thickness of physical metasurfaces. A simple analytical approach is used to extract the bianisotropic susceptibility tensor of concentric, multilayered, magneto-dielectric shell. Plane wave scattering by a physical metasurface constructed of four segments of multilayered, magneto-dielectric metasurface scatterers is used as an example problem to validate cylindrical IEGSTC. A second example considers an opening on the cylindrical metasurface, confirming IE-GSTC can handle metasurfaces with openings. Good agreement is obtained between IE-GSTC results and full wave simulation results for both cases.</div>

Application of cylindrical IE-GSTC to physical metasurfaces

<div>This work validates cylindrical IE-GSTC by applying it to physical metasurfaces, i.e. metasurfaces defined by material properties and dimensions rather than by susceptibility tensor components. Previously reported IE-GSTC which was formulated for zero thickness GSTC discontinuity is extended to handle finite thickness of physical metasurfaces. A simple analytical approach is used to extract the bianisotropic susceptibility tensor of concentric, multilayered, magneto-dielectric shell. Plane wave scattering by a physical metasurface constructed of four segments of multilayered, magneto-dielectric metasurface scatterers is used as an example problem to validate cylindrical IEGSTC. A second example considers an opening on the cylindrical metasurface, confirming IE-GSTC can handle metasurfaces with openings. Good agreement is obtained between IE-GSTC results and full wave simulation results for both cases.</div>

Application of cylindrical IE-GSTC to physical metasurfaces

<div>This work validates cylindrical IE-GSTC by applying it to physical metasurfaces, i.e. metasurfaces defined by material properties and dimensions rather than by susceptibility tensor components. Previously reported IE-GSTC which was formulated for zero thickness GSTC discontinuity is extended to handle finite thickness of physical metasurfaces. A simple analytical approach is used to extract the bianisotropic susceptibility tensor of concentric, multilayered, magneto-dielectric shell. Plane wave scattering by a physical metasurface constructed of four segments of multilayered, magneto-dielectric metasurface scatterers is used as an example problem to validate cylindrical IEGSTC. A second example considers an opening on the cylindrical metasurface, confirming IE-GSTC can handle metasurfaces with openings. Good agreement is obtained between IE-GSTC results and full wave simulation results for both cases.</div>

Singular integral equations in plane wave scattering by infinite graphene strip grating with brake of periodicity

In this paper, the solution of the H-polarized wave scattering problem by infinite graphene strip grating is obtained. The structure is periodic except two neighboring strips. The distance between these two strips is arbitrary. In particular, such a problem allows to quantify the mutual interaction of graphene strips in the array. The total field is represented as a superposition of the field of currents on the ideally-periodic grating and correction currents induced by the shift of the strips. The analysis is based on the convergent method of singular integral equations. It enables us to study the influence of the correction currents in a wide range from 10 GHz to 6 THz. It is shown that the interaction between graphene strips is strong near plasmon resonances and near the Rayleigh anomaly.