相关论文: Energy evolution of multi-symplectic methods for M…

In this paper, we investigate the energy problem in general relativity using approximate Lie symmetry methods for differential equations. This procedure is applied to Bardeen model (the regular black hole solution). Here we are forced to…

We consider a parameter dependent family of damped hyperbolic equations with interesting limit behavior: the system approaches steady states exponentially fast and for parameter to zero the solutions converge to that of a parabolic limit…

In this work we study linear Maxwell equations with time- and space-dependent matrix-valued permittivity and permeability on domains with a perfectly conducting boundary. This leads to an initial boundary value problem for a first order…

By fixing a reference frame in spacetime, it is possible to split the Euler-Lagrange equations associated with a degenerate Lagrangian into purely evolutionary equations and constraints on the allowed Cauchy data with respect to the notion…

Motivated by various applications, this article develops the notion of boundary control for Maxwell's equations in the frequency domain. Surface curl is shown to be the appropriate regularization in order for the optimal control problem to…

We develop a finite volume method for Maxwell's equations in materials whose electromagnetic properties vary in space and time. We investigate both conservative and non-conservative numerical formulations. High-order methods accurately…

Electromagnetism plays an important role in a variety of applications in gravity that we wish to investigate. To that end, in this work, we present an implementation of the Maxwell equations within the adaptive-mesh pseudospectral numerical…

In this paper, we mainly discuss asymptotic profiles of solutions to a class of abstract second-order evolution equations of the form $u''+Au+u'=0$ in real Hilbert spaces, where $A$ is a nonnegative selfadjoint operator. The main result is…

This letter studies symmetric and symplectic exponential integrators when applied to numerically computing nonlinear Hamiltonian systems. We first establish the symmetry and symplecticity conditions of exponential integrators and then show…

Hamilton's equations are fundamental for modeling complex physical systems, where preserving key properties such as energy and momentum is crucial for reliable long-term simulations. Geometric integrators are widely used for this purpose,…

In this paper we consider the spatial semi-discretization of conservative PDEs. Such finite dimensional approximations of infinite dimensional dynamical systems can be described as flows in suitable matrix spaces, which in turn leads to the…

We study the dynamics of expansion of the homogeneous isotropic Universe and the evolution of its components in the model with nonminimally coupled dynamical dark energy. Dark energy, like the other components of the Universe, is described…

Quantum 3D R-matrix in the classical (i.e. functional) limit gives a symplectic map of dynamical variables. The corresponding 3D evolution model is considered. An auxiliary problem for it is a system of linear equations playing the role of…

Despite its widespread significance, the temporal coupled-mode theory (CMT) lacks a foundational validation based on electromagnetic principles and stands as a phenomenological theory relying on fitted coupling coefficients. We employ an ab…

We consider a finite element approximation for a system consisting of the evolution of a closed planar curve by forced curve shortening flow coupled to a reaction-diffusion equation on the evolving curve. The scheme for the curve evolution…

We will provide detailed arguments showing that the set of Maxwell equations, and the corresponding wave equations, do not properly describe the evolution of electromagnetic wave-fronts. We propose a nonlinear corrected version that is…

Starting from the Maxwell-Lorentz equations, Poynting's theorem is reconsidered. The energy flux vector is introduced as S_e=(E x B)/mu_0 instead of E x H, because only by this choice the energy dissipation can be related to the balance of…

Symmetric method and symplectic method are classical notions in the theory of Runge-Kutta methods. They can generate numerical flows that respectively preserve the symmetry and symplecticity of the continuous flows in the phase space.…

In this paper we propose and analyze finite element discontinuous Galerkin methods for the one- and two-dimensional stochastic Maxwell equations with multiplicative noise. The discrete energy law of the semi-discrete DG methods were…

We investigate spherically symmetric cosmological models in Einstein-aether theory with a tilted (non-comoving) perfect fluid source. We use a 1+3 frame formalism and adopt the comoving aether gauge to derive the evolution equations, which…