Related papers: Model and computational advancements to full vecto…
We present an arbitrary-order spectral element method for general-purpose simulation of non-overturning water waves, described by fully nonlinear potential theory. The method can be viewed as a high-order extension of the classical finite…
We present a real-time propagation method for computing linear and nonlinear optical properties of molecules based on the Bethe-Salpeter equation. The method follows the time evolution of the one-particle density matrix under an external…
We consider problems related to initial meshing and adaptive mesh refinement for the electromagnetic simulation of various structures. The quality of the initial mesh and the performance of the adaptive refinement are of great importance…
A finite element method is presented to compute time harmonic microwave fields in three dimensional configurations. Nodal-based finite elements have been coupled with an absorbing boundary condition to solve open boundary problems. This…
Manufacturing end-of-fiber optical components able to realize optical functions ranging from a simple lens to more complex functions such as mode selective components is a decisive but \emph{a priori} complex task owing to the fiber core…
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 discuss a multiscale Galerkin approximation scheme for a system of coupled quasilinear parabolic equations. These equations arise from the upscaling of a pore scale filtration combustion model under the assumptions of large Damkh\"oler…
We make progress towards a 3D finite-element model for the magnetization of a high temperature superconductor (HTS): We suggest a method that takes into account demagnetisation effects and flux creep, while it neglects the effects…
The analysis of a delayed generalized Burgers-Huxley equation (a non-linear advection-diffusion-reaction problem) with weakly singular kernels is carried out in this work. Moreover, numerical approximations are performed using the…
We present a full-vector finite element method (FEM) mode solver for dielectric waveguides based on a mixed Nedelec-Lagrange discretization of Maxwell's curl equations in the frequency domain. The formulation combines edge elements for…
High-gain Free Electron Laser (FEL) is one of the many electron-beam instabilities that have a number of common features linking the shot noise, the amplification and the saturation. In this paper, we present a new, model-independent…
We propose and analyze an augmented mixed finite element method for the pseudostress-velocity formulation of the stationary convective Brinkman-Forchheimer problem in $\mathrm{R}^d$, $d\in \{2,3\}$. Since the convective and Forchheimer…
We theoretically study prospects and limitations of a new route towards macroscopic scale laser refrigeration based on exciplex-mediated frequency up-conversion in gas filled hollow-core fibres. Using proven quantum optical rate equations…
Multimode fibers provide a promising platform for realizing high-power laser amplifiers with suppressed nonlinearities and instabilities. The potential degradation of optical beam quality has been a major concern for highly multimode fiber…
Higher-abelian gauge theories associated with Cheeger-Simons differential characters are studied on compact manifolds without boundary. The paper consists of two parts: First the functional integral formulation based on zeta function…
We propose an explicit iterative leap-frog discontinuous Galerkin method for time-domain Maxwell's equations in anisotropic materials and derive its convergence properties. The a priori error estimates are illustrated by numerical means in…
From a mathematical perspective, the extraordinary properties of metamaterials are often reflected in the coefficients of the governing partial differential equations (PDEs). These coefficients may fall outside the assumptions of classical…
Accurate simulation of nonlinear acoustic waves is essential for the continued development of a wide range of (high-intensity) focused ultrasound applications. This article explores mixed finite element formulations of classical strongly…
It is known that both linear and nonlinear optical phenomena can be produced when the plasmon in metallic nanostructures are excited by the external electromagnetic waves. In this work, a coupled system of Maxwell equations and a gas…
In outdoor acoustics, the calculations of sound propagating in air can be computationally heavy if the domain is chosen large enough to fulfil the Sommerfeld radiation condition. By strategically truncating the computational domain with a…