Related papers: A Vectorial Envelope Maxwell Formulation for Elect…
High-frequency wave propagation is often modelled by nonlinear Friedrichs systems where both the differential equation and the initial data contain the inverse of a small parameter $\varepsilon$, which causes oscillations with wavelengths…
We consider an elastic model for a circular arch that incorporates membrane, transverse shear, and bending effects. The central line of the arch is partitioned into elements, and an ultra-weak variational formulation is developed alongside…
The recently re-discovered multipole vector approach to understanding the harmonic decomposition of the cosmic microwave background traces its roots to Maxwell's Treatise on Electricity and Magnetism. Taking Maxwell's directional derivative…
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…
We show that arbitrary 3D electromagnetic fields are transient solutions to Maxwell's equations and provide a simple equation to find how the field evolves over time. Multiple 3D fields can be realized at different times by superposing with…
A new method to find the propagation equation system governing the scattering of an electromagnetic wave by a nonlinear medium is proposed. The aim is to let the effects appear spontaneously, deleting as far as possible the phenomenological…
This paper describes a class of shape optimization problems for optical metamaterials comprised of periodic microscale inclusions composed of a dielectric, low-dimensional material suspended in a non-magnetic bulk dielectric. The shape…
A time domain electric field volume integral equation (TD-EFVIE) solver is proposed for analyzing electromagnetic scattering from dielectric objects with Kerr nonlinearity. The nonlinear constitutive relation that relates electric flux and…
Numerical simulation of wave propagation in an infinite medium is made possible by surrounding a finite region by a perfectly matched layer (PML). Using this approach a generalized three-dimensional (3D) formulation is proposed for…
This work represents the first endeavor in using ultraweak formulations to implement high-order polygonal finite element methods via the discontinuous Petrov-Galerkin (DPG) methodology. Ultraweak variational formulations are nonstandard in…
The robustness of XRD methods for the determination of the lattice parameters of crystals is well established. These methods have been extended to helical atomic structures using twisted x-rays \cite{friesecke_twisted_2016}. Building on an…
A Discontinuous Galerkin (DG) Finite Element Method (FEM) approach for the 3D time dependent Maxwell equations in unbounded domains is presented. The method (implemented in the FEM library NGsolve) is based on the covariant transformation…
In this paper, we generalize the idea in our previous work for the Vlasov-Amp\`{e}re (VA) system \cite{cheng_va} and develop energy-conserving discontinuous Galerkin (DG) methods for the Vlasov-Maxwell (VM) system. The VM system is a…
An error analysis of a mixed discontinuous Galerkin (DG) method with Brezzi numerical flux for the time-harmonic Maxwell equations with minimal smoothness requirements is presented. The key difficulty in the error analysis for the DG method…
The time-harmonic Maxwell equations at high wavenumber $k$ are discretized by edge elements of degree $p$ on a mesh of width $h$. For the case of a ball and exact, transparent boundary conditions, we show quasi-optimality of the Galerkin…
With the advent of PW class lasers, the very large laser intensities attainable on-target should enable the production of intense high order Doppler harmonics from relativistic laser-plasma mirrors interactions. At present, the modeling of…
We apply the method of slowly-varying amplitudes of the electrical and magnet fields to integro-differential system of nonlinear Maxwell equations. The equations are reduced to system of differential Nonlinear Maxwell amplitude Equations…
We propose a modified Trefftz Discontinuous Galerkin (TDG) method for approximating a time-harmonic acoustic scattering problem in an infinitely elongated waveguide. In the waveguide we suppose there is a bounded, penetrable and possibly…
The time domain enclosure method is one of analytical methods for inverse obstacle problems governed by partial differential equations in the time domain. This paper considers the case when the governing equation is given by the Maxwell…
We extend the $t-z$ mapping formalism of time-dependent paraxial optics by identifying configurations displaying a synthetic magnetic vector potential, leading to a non-trivial band topology in propagating geometries. We consider an…