Related papers: Application of the Covariant projection finite ele…
In many time-harmonic electromagnetic wave problems, the considered geometry exhibits an axial symmetry. In this case, by exploiting a Fourier expansion along the azimuthal direction, fully three-dimensional (3D) calculations can be carried…
Rigorous computer simulations of propagating electromagnetic fields have become an important tool for optical metrology and optics design of nanostructured components. As has been shown in previous benchmarks some of the presently used…
As inelastic structures are ubiquitous in many engineering fields, a central task in computational mechanics is to develop accurate, robust and efficient tools for their analysis. Motivated by the poor performances exhibited by standard…
The wave function of a composite system is defined in relativity on a space-time surface. In the explicitly covariant light-front dynamics, reviewed in the present article, the wave functions are defined on the plane $\omega \cd x=0$, where…
Spatial coordinate transformation is a suitable tool for the design of complex electromagnetic structures. In this paper, we define three spatial coordinate transformations which show the possibility of designing a taper between two…
In this chapter, we demonstrate a general formulation of the Finite Element Method allowing to calculate the diffraction efficiencies from the electromagnetic field diffracted by arbitrarily shaped gratings embedded in a multilayered stack…
We show how two-dimensional mixed finite element methods that satisfy the conditions of finite element exterior calculus can be used for the horizontal discretisation of dynamical cores for numerical weather prediction on pseudo-uniform…
In this work, we present an efficient numerical implementation of the finite element method for modal analysis that leverages various symmetry operations, including spatial symmetry in point groups and space-time symmetry in…
A simple theory of the covariant derivatives, deformed derivatives and relative covariant derivatives of extensor fields is present using algebraic and analytical tools developed in previous papers. Several important formulas are derived.
We discuss analytically and numerically the propagation and energy transmission of electromagnetic waves caused by the coupling of surface plasmon polaritons (SPPs) between two spatially separated layers of 2D materials, such as graphene,…
Mass production of photonic integrated circuits requires high-throughput wafer-level testing. We demonstrate that optical probes equipped with 3D-printed elements allow for efficient coupling of light to etched facets of nanophotonic…
In this paper, we study an adaptive finite element method for a class of a nonlinear eigenvalue problems that may be of nonconvex energy functional and consider its applications to quantum chemistry. We prove the convergence of adaptive…
A new approach for analyzing waveguide junctions containing conductive cylindrical objects is proposed. The algorithm is based on mode matching technique using local projection functions, which improves the numerical conditioning of the…
We discuss a way to exploit the conformal mapping to study the response of a finite metallic element of arbitrary shape to an external electromagnetic field at finite frequencies. This provides a simple way to study different physics issues…
The finite element method is widely used in simulations of various fields. However, when considering domains whose extent differs strongly in different spatial directions a finite element simulation becomes computationally very expensive…
A systematic expression quantifying the wave energy skewing phenomenon as a function of the mechanical characteristics of a non-isotropic structure is derived in this study. A structure of arbitrary anisotropy, layering and geometric…
The transformation media concept based on the form-invariant Maxwell's equations under coordinate transformations has opened up new possibilities to manipulate the electromagnetic fields. In this paper we report on applying the…
The finite element method (FEM) is applied to obtain numerical solutions to a recently derived nonlinear equation for the shallow water wave problem. A weak formulation and the Petrov-Galerkin method are used. It is shown that the FEM gives…
The finite element analysis of high frequency vibrations of quartz crystal plates is a necessary process required in the design of quartz crystal resonators of precision types for applications in filters and sensors. The anisotropic…
In this work we present an extension of the Virtual Element Method with curved edges for the numerical approximation of the second order wave equation in a bidimensional setting. Curved elements are used to describe the domain boundary, as…