Related papers: Closed-form analytical solution for the transfer m…
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…
This paper is devoted to the numerical validation of an explicit finite-difference scheme for the integration in time of Maxwell's equations in terms of the sole electric field, using standard linear finite elements for the space…
Semi-discrete and fully discrete mixed finite element methods are considered for Maxwell-model-based problems of wave propagation in linear viscoelastic solid. This mixed finite element framework allows the use of a large class of existing…
Geometric particle-in-cell discretizations have been derived based on a discretization of the fields that is conforming with the de Rham structure of the Maxwell's equation and a standard particle-in-cell ansatz for the fields by deriving…
In this work, we obtain closed expressions for the transfer matrix and the transmittance of electromagnetic waves propagating in finite 1D anisotropic periodic stratified media with an arbitrary number of cells. By invoking the…
Consider a rectangular matrix describing some type of communication or transportation between a set of origins and a set of destinations, or a classification of objects by two attributes. The problem is to infer the entries of the matrix…
A mimetic spectral element discretization, utilizing a novel Galerkin projection Hodge star operator, of the macroscopic Maxwell equations in Hamiltonian form is presented. The idea of splitting purely topological and metric dependent…
We present a numerical approach to efficiently calculate spin-wave dispersions and spatial mode profiles in magnetic waveguides of arbitrarily shaped cross section with any non-collinear equilibrium magnetization which is translationally…
We present a numerically stable re-formulization of the transfer matrix method (TMM). The iteration form of the traditional TMM is transformed into solving a set of linear equations. Our method gains the new ability of calculating accurate…
We consider a coefficient inverse problem for the dielectric permittivity in Maxwell's equations, with data consisting of boundary measurements of one or two backscattered or transmitted waves. The problem is treated using a Lagrangian…
Density matrices are powerful mathematical tools for the description of closed and open quantum systems. Recently, methods for the direct computation of density matrix elements in scalar quantum field theory were developed based on thermo…
Maxwell's equations are a system of partial differential equations that govern the laws of electromagnetic induction. We study a mimetic finite-difference (MFD) discretization of the equations which preserves important underlying physical…
The $\phi$-divergence-based moment method was recently introduced Abdelmalik et al. (2023) for the discretization of the radiative transfer equation. At the continuous level, this method is very close to the entropy-based MN methods and…
We introduce a numerical strategy to efficiently solve the out-of-equilibrium Dyson equation in the transient regime. By discretizing the equation into a compact matrix form and applying state-of-the-art matrix compression techniques, we…
We clarify the algebraic structure of continuous and discrete quasi-exactly solvable spectral problems by embedding them into the framework of the quantum inverse scattering method. The quasi-exactly solvable hamiltonians in one dimension…
In a recent article the authors showed that the radiative Transfer equations with multiple frequencies and scattering can be formulated as a nonlinear integral system. In the present article, the formulation is extended to handle reflective…
By expressing the time-independent Schrodinger equation in one dimension as a system of two first-order differential equations, the transfer matrix for a rectangular potential barrier is obtained making use of the matrix exponential. It is…
We develop a systematic field-theoretical approach to open quantum systems based on condensed-matter many-body methods. The time evolution of the reduced density matrix for the open quantum system is determined by a transmission matrix.…
This paper provides a rigorous analysis of boundary element methods for the magnetic field integral equation on Lipschitz polyhedra. The magnetic field integral equation is widely used in practical applications to model electromagnetic…
A finite element methodology for large classes of variational boundary value problems is defined which involves discretizing two linear operators: (1) the differential operator defining the spatial boundary value problem; and (2) a Riesz…