相关论文: Homogenization of multiscale Maxwell wave equation…
The present paper concerns a space-time homogenization problem for nonlinear diffusion equations with periodically oscillating (in space and time) coefficients. Main results consist of corrector results (i.e., strong convergences of…
This paper aims at an accurate and efficient computation of effective quantities, e.g., the homogenized coefficients for approximating the solutions to partial differential equations with oscillatory coefficients. Typical multiscale methods…
We pursue a low-wavenumber, second-order homogenized solution of the time-harmonic wave equation at both low and high frequency in periodic media with a source term whose frequency resides inside a band gap. Considering the wave motion in…
Time-harmonic solutions to the wave equation can be computed in the frequency or in the time domain. In the frequency domain, one solves a discretized Helmholtz equation, while in the time domain, the periodic solutions to a discretized…
When anisotropy is involved, the wave equation becomes simultaneous partial differential equations that are not easily solved. Moreover, when the anisotropy occurs due to both permittivity and permeability, these equations are insolvable…
In this paper, we develop a computational multiscale to solve the parabolic wave approximation with heterogeneous and variable media. Parabolic wave approximation is a technique to approximate the full wave equation. One benefit of the…
A family of the so-called Maxwell times which arises in the contexto of Higher-Order Generalized Hydrodynamics (also called Mesoscopic Hydro-Thermodynamics) is evidenced. This is done in the framework of a HOGH build within a statistical…
In this work, we design and investigate contrast-independent partially explicit time discretizations for wave equations in heterogeneous high-contrast media. We consider multiscale problems, where the spatial heterogeneities are at subgrid…
In this paper, we discuss a general framework for multicontinuum homogenization. Multicontinuum models are widely used in many applications and some derivations for these models are established. In these models, several macroscopic…
Hydromagnetic turbulence produced during phase transitions in the early universe can be a powerful source of stochastic gravitational waves (GWs). GWs can be modelled by the linearised spatial part of the Einstein equations sourced by the…
The Maxwell's equations are solved when it has an inhomogeneous terms as a source. The solution is very general in a sense that it handles arbitrary current source and anisotropic media. The calculation is carried out in the k-domain after…
The Helmholtz equation is notoriously difficult to solve with standard numerical methods, increasingly so, in fact, at higher frequencies. Controllability methods instead transform the problem back to the time-domain, where they seek the…
The generation of second and third harmonics by an acoustic wave propagating along one dimension in a weakly nonlinear elastic medium that is loaded harmonically in time with frequency $\omega_0$ at a single point in space, is analyzed by…
Consider the wave equation with heterogeneous coefficients in the homogenization regime. At large times, the wave interacts in a nontrivial way with the heterogeneities, giving rise to effective dispersive effects. The main achievement of…
We couple the mixed variational problem for the generalized Hodge-Helmholtz or Hodge-Laplace equation posed on a bounded three-dimensional Lipschitz domain with the first-kind boundary integral equation arising from the latter when constant…
Multiscale modelling aims to systematically construct macroscale models of materials with fine microscale structure. However, macroscale boundary conditions are typically not systematically derived, but rely on heuristic arguments,…
Homogenisation of global $\mathcal{A}^\epsilon$ and exponential $\mathcal{M}^\epsilon$ attractors for the damped semi-linear anisotropic wave equation $\partial_t^2 u^\epsilon +\gamma\partial_t u^\epsilon-{\rm div} \left(a\left(…
In the present work, we consider multi-scale computation and convergence for nonlinear time-dependent thermo-mechanical equations of inhomogeneous shells possessing temperature-dependent material properties and orthogonal periodic…
We study the scaling behaviour of a class of compatible two-well problems for higher order, homogeneous linear differential operators. To this end, we first deduce general lower scaling bounds which are determined by the vanishing order of…
We consider a simple two-dimemsional harmonic lattice with random, independent and identically distributed masses. Using the methods of stochastic homogenization, we show that solutions with long wave initial data converge in an appropriate…