相关论文: Pseudospectral implementation of the Einstein-Maxw…
We present a new pseudospectral code, bamps, for numerical relativity written with the evolution of collapsing gravitational waves in mind. We employ the first order generalized harmonic gauge formulation. The relevant theory is reviewed…
We use partial differential equations (PDEs) to describe physical systems. In general, these equations include evolution and constraint equations. One method used to find solutions to these equations is the Free-evolution approach, which…
The Einstein and Maxwell equations are both systems of hyperbolic equations which need to satisfy a set of elliptic constraints throughout evolution. However, while electrodynamics (EM) and magnetohydrodynamics (MHD) have benefited from a…
We study asymptotically constrained systems for numerical integration of the Einstein equations, which are intended to be robust against perturbative errors for the free evolution of the initial data. First, we examine the previously…
Rapid growth of constraints is often observed in free evolutions of highly gravitating systems. To alleviate this problem we investigate the effect of adding spatial derivatives of the constraints to the right hand side of the evolution…
In the present work, we demonstrate how the pseudoinverse concept from linear algebra can be used to represent and analyze the boundary conditions of linear systems of partial differential equations. This approach has theoretical and…
Maxwell-Amp\`{e}re-Nernst-Planck (MANP) equations were recently proposed to model the dynamics of charged particles. In this study, we enhance a numerical algorithm of this system with deep learning tools. The proposed hybrid algorithm…
We investigate how the accuracy and stability of numerical relativity simulations of 1D colliding plane waves depends on choices of equation formulations, gauge conditions, boundary conditions, and numerical methods, all in the context of a…
This is the first paper in a series aimed to implement boundary conditions consistent with the constraints' propagation in 3D numerical relativity. Here we consider spherically symmetric black hole spacetimes in vacuum or with a minimally…
The article deals with electrodynamics in the presence of anisotropic materials having scalar wave impedance. Maxwell's equations written for differential forms over a 3-manifold are analysed. The system is extended to a Dirac type first…
Computational electromagnetics (CEM) is employed to numerically solve Maxwell's equations, and it has very important and practical applications across a broad range of disciplines, including biomedical engineering, nanophotonics, wireless…
We present three-dimensional simulations of Einstein equations implementing a symmetric hyperbolic system of equations with dynamical lapse. The numerical implementation makes use of techniques that guarantee linear numerical stability for…
Systems of PDEs comprised of a combination of constraints and evolution equations are ubiquitous in physics. For both theoretical and practical reasons, such as numerical integration, it is desirable to have a systematic understanding of…
We prove sharp wavenumber-explicit error bounds for first- or second-family-N\'ed\'elec-element (a.k.a. edge-element) conforming discretisations, of arbitrary (fixed) order, of the variable-coefficient time-harmonic Maxwell equations posed…
This work is on the numerical approximation of incoming solutions to Maxwell's equations with dissipative boundary conditions whose energy decays exponentially with time. Such solutions are called asymptotically disappearing (ADS) and they…
We consider the estimation of an i.i.d. (possibly non-Gaussian) vector $\xbf \in \R^n$ from measurements $\ybf \in \R^m$ obtained by a general cascade model consisting of a known linear transform followed by a probabilistic componentwise…
The constraint equations in Maxwell theory are investigated. In analogy with some recent results on the constraints of general relativity it is shown, regardless of the signature and dimension of the ambient space, that the "divergence of a…
Inferring electromagnetic propagation characteristics within the marine atmospheric boundary layer (MABL) from data in real time is crucial for modern maritime navigation and communications. The propagation of electromagnetic waves is well…
In Yang et al. [Nature 576, 248 (2019)], the authors introduced a general theoretical framework for nanoscale electromagnetism based on Feibelman parameters. Here quantum effects of the optically excited electrons at the interface between…
The governing equations of Maxwell electrodynamics in multi-dimensional spaces are derived from the variational principle of least action which is applied to the action function of the electromagnetic field. The Hamiltonian approach for the…