Related papers: A convolution quadrature method for Maxwell's equa…
Multiscale dynamics are ubiquitous in applications of modern science. Because of time scale separation between relatively small set of slowly evolving variables and (typically) much larger set of rapidly changing variables, direct numerical…
We developed fast direct solver for 3D Helmholtz and Maxwell equations in layered medium. The algorithm is based on the ideas of cyclic reduction for separable matrices. For the grids with major uniform part (within the survey domain in the…
This paper contains construction and analysis a finite element approximation for convection dominated diffusion problems with full coefficient matrix on general simplicial partitions in $R^d$, $d=2,3$. This construction is quite close to…
An implicit Euler finite-volume scheme for general cross-diffusion systems with volume-filling constraints is proposed and analyzed. The diffusion matrix may be nonsymmetric and not positive semidefinite, but the diffusion system is assumed…
Two methods are explained to exactly solve Maxwell's equations where permittivity, permeability and conductivity may vary in space. In the constitutive relations, retardation is regarded. If the material properties depend but on one…
We propose a novel formulation for parametric finite element methods to simulate surface diffusion of closed curves, which is also called as the curve diffusion. Several high-order temporal discretizations are proposed based on this new…
The Douglas--Rachford and Peaceman--Rachford splitting methods are common choices for temporal discretizations of evolution equations. In this paper we combine these methods with spatial discretizations fulfilling some easily verifiable…
This paper is devoted to the complete convergence study of the finite-element approximation of Maxwell's equations in the case where the magnetic permeability is constant. Standard linear finite elements for the space discretization are…
The features of propagation of intense waves are of great interest for theory and experiment in electrodynamics and acoustics. The behavior of nonlinear waves in a bounded volume is of especial importance and, at the same time, is an…
The magnetotelluric approximation of the Maxwell's equations is used to model the propagation of low frequency electro-magnetic waves in the Earth's subsurface, with the purpose of reconstructing the presence of mineral or oil deposits. We…
In this paper we want to propose practical numerical methods to solve a class of initial-boundary problem of time-space fractional convection-diffusion equations (TSFCDEs). To start with, an implicit difference method based on two-sided…
This paper presents a mathematical foundation for physical models in nonlinear optics through the lens of evolutionary equations. It focuses on two key concepts: well-posedness and exponential stability of Maxwell equations, with models…
A hydrogeological model for the spread of pollution in an aquifer is considered. The model consists in a convection-diffusion-reaction equation involving the dispersion tensor which depends nonlinearly of the fluid velocity. We introduce an…
The first part of this paper introduces sufficient conditions to determine conservation laws of diffusion equations of arbitrary fractional order in time. Numerical methods that satisfy a discrete analogue of these conditions have…
We describe an exact and highly efficient numerical algorithm for solving a special but important class of convection-diffusion equations. These equations occur in many problems in physics, chemistry, or biology, and they are usually hard…
The main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell-Lorentz electromagnetics and discuss its immediate analytical and numerical…
This paper develops a strong computational approach to simulate a three-dimensional nonlinear radiation-conduction model in optically thick media, subject to suitable initial and boundary conditions. The space derivatives are approximated…
The advection-diffusion and wave equations are the fundamental equations governing any physical law and therefore arise in many areas of physics and astrophysics. For complex problems and geometries, only numerical simulations can give…
We extend the usual derivation of the wave equation from Maxwell's equations in vacuum to the case of electromagnetic fields in dispersive homogeneous isotropic linear media. Usually, dispersive properties of materials are studied in…
Generalized impedance boundary conditions are effective, approximate boundary conditions that describe scattering of waves in situations where the wave interaction with the material involves multiple scales. In particular, this includes…