Related papers: A Space-Time Approach for the Time-Domain Simulati…
Employing a relativistic rotational transformation to study and analyze rotational phenomena, instead of the rotational transformations based on consecutive Lorentz transformations and Fermi coordinates, leads to different predictions. In…
A short review of the method for the tensor reduction of Feynman integrals based on recurrence relations with respect to space-time dimension d- is given. A solution of the difference equation with respect to d for the n - point one-loop…
Time-domain wave scattering in an unbounded two-dimensional acoustic medium by sound-hard scatterers is considered. Two canonical geometries, namely a split-ring resonator (SRR) and an array of cylinders, are used to highlight the theory,…
Stability and convergence analysis for the domain decomposition finite element/finite difference (FE/FD) method is presented. The analysis is designed for semi-discrete finite element scheme for the time-dependent Maxwell's equations. The…
Maxwell equations describe the propagation of electromagnetic waves and are therefore fundamental to understanding many problems encountered in the study of antennas and electromagnetics. The aim of this paper is to propose and analyse an…
A framework for exponential time discretization of the multilayer rotating shallow water equations is developed in combination with a mimetic discretization in space. The method is based on a combination of existing exponential time…
We revise the finite element formulation for Lagrange, Raviart- Thomas, and Taylor-Hood finite element spaces. We solve Laplace equation in first and second order formulation, and compare the solutions obtained with Lagrange and…
In this article, we analyze semi-discrete finite element approximation and full discretization of a fourth-order stochastic pseudo-parabolic equation in a bounded convex polygonal domain driven by additive Wiener noise. We use the finite…
In the context of the natural splitting, the standard relative dynamics can be expressed in terms of gravito-electromagnetic fields, which allow to formally introduce a gravito-magnetic Aharonov-Bohm effect. We showed elsewhere that this…
A novel finite element method for the approximation of Maxwell's equations over hybrid two-dimensional grids is studied. The choice of appropriate basis functions and numerical quadrature leads to diagonal mass matrices which allow for…
In the framework of spacetime with torsion and without curvature, the Dirac particle spin precession in the rotational system is studied. We write out the equivalent tetrad of rotating frame, in the polar coordinate system, through…
The discretization approximation method commonly used to simulate the dynamics of quantum system coupled to the environment in continuum often suffers from the periodically partial recovery of initial state because of the effect of finite…
Recently, split ring-resonators (SRR's) have been realized experimentally in the near infrared (NIR) and optical regime. In this contribution we numerically investigate light propagation through an array of metallic SRR's in the NIR and…
The rotating disk problem is analyzed on the premise that proper interpretation of experimental evidence leads to the conclusion that the postulates upon which relativity theory is based, particularly the invariance of the speed of light,…
We apply the ``consistent discretization'' approach to general relativity leaving the spatial slices continuous. The resulting theory is free of the diffeomorphism and Hamiltonian constraints, but one can impose the diffeomorphism…
In this paper, we propose a numerical method to approximate the solution of the time-dependent Schr\"odinger equation with periodic boundary condition in a high-dimensional setting. We discretize space by using the Fourier pseudo-spectral…
Non-time-orthogonal analysis of rotating frames is applied to objects in gravitational orbits and found to be internally consistent. The object's surface speed about its axis of rotation, but not its orbital speed, is shown to be readily…
We propose a novel mixed finite-element formulation for geometrically exact (Simo--Reissner) beams that introduces the moment vector as additional independent field. The specific mixed form allows for an element-local, discontinuous…
In the literature on quantum reference frames, the internal (relative) properties of a system are defined as those which are preserved under an arbitrary change of reference frame. For a system of quantum spins, these are all properties…
It is described, explicitly, how a popular, commercially-available software package for solving partial-differential-equations (PDEs), as based on the finite-element method (FEM), can be configured to calculate the frequencies and fields of…