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We derive and analyze a broad class of finite element methods for numerically simulating the stationary, low Reynolds number flow of concentrated mixtures of several distinct chemical species in a common thermodynamic phase. The underlying…
A new semi-analytical iterative scheme is proposed in this work for solving the generalized Peierls-Nabarro model. The numerical method developed here exploits certain basic properties of the Hilbert transform to achieve the desired…
In this paper we describe a method to compute Generalized Polarization Tensors. These tensors are the coefficients appearing in the multipolar expansion of the steady state voltage perturbation caused by an inhomogeneity of constant…
We study the numerical approximation by space-time finite element methods of a multi-physics system coupling hyperbolic elastodynamics with parabolic transport and modeling poro- and thermoelasticity. The equations are rewritten as a…
We present a new time discretization scheme adapted to the structure of GENERIC systems. The scheme is variational in nature and is based on a conditional incremental minimization. The GENERIC structure of the scheme provides stability and…
The doping of semiconductor materials is a fundamental part of modern technology, but the classical approaches have in many cases reached their limits both in regard to achievable charge carrier density, as well as mobility. Modulation…
The application of discontinuous Galerkin (DG) schemes to hyperbolic systems of conservation laws requires a careful interplay between space discretization, carried out with local polynomials and numerical fluxes at inter-cells, and…
In this article we propose and numerically implement a mathematical model for the simulation of three-dimensional semiconductor devices characterized by an heterogeneous material structure. The model consists of a system of nonlinearly…
We present a new fully first order strongly hyperbolic representation of the BSSN formulation of Einstein's equations with optional constraint damping terms. We describe the characteristic fields of the system, discuss its hyperbolicity…
In this work, we consider the generalized quantum electrodynamics proposed by Podolsky in Heisenberg picture via Kallen methodology. We investigate the effects of higher-order derivatives to understand the qualitative and quantitative…
To be practical, semiconductors need to be doped. Sometimes, to nearly degenerate levels, e.g. in applications such as thermoelectric, transparent electronics or power electronics. However, many materials with finite band gaps are not…
In an electrostatic simulation, an equipotential condition with an undefined/floating potential value has to be enforced on the surface of an isolated conductor. If this conductor is charged, a nonzero charge condition is also required.…
This work considers the Galerkin approximation and analysis for a hyperbolic integrodifferential equation, where the non-positive variable-sign kernel and nonlinear-nonlocal damping with both the weak and viscous damping effects are…
Interactive global illumination remains a challenge in radiometrically- and geometrically-complex scenes. Specialized sampling strategies are effective for specular and near-specular transport because the scattering has relatively low…
We have derived a variational principle that defines the nonequilibrium steady-state transport across a correlated impurity mimicking, e.g., a quantum dot coupled to biased leads. This variational principle has been specialized to a…
We adapt the Gradient Discretisation Method (GDM), originally designed for elliptic and parabolic partial differential equations, to the case of a linear scalar hyperbolic equations. This enables the simultaneous design and convergence…
This paper investigates an efficient exponential integrator generalized multiscale finite element method for solving a class of time-evolving partial differential equations in bounded domains. The proposed method first performs the spatial…
A self-consistent model of bipolar charge-carrier injection and transport processes in a semiconductor/insulator/conductor system is developed which incorporates space-charge effects in the description of the injection process. The amount…
We propose extensions and improvements of the statistical analysis of distributed multipoles (SADM) algorithm put forth by Chipot et al. in [6] for the derivation of distributed atomic multipoles from the quantum-mechanical electrostatic…
The convergence of iterative schemes to achieve self-consistency in mean field problems such as the Schr\"odinger-Poisson equation is notoriously capricious. It is particularly difficult in regimes where the non-linearities are strong such…