Related papers: A mixed-dimensional model for the electrostatic pr…
Motivated by the paraxial narrow-angle approximation of the Helmholtz equation in domains of variable topography that appears as an important application in Underwater Acoustics, we analyze a general Schr\"odinger-type equation posed on…
In this paper, we consider acoustic or electromagnetic scattering in two dimensions from an infinite three-layer medium with thousands of wavelength-size dielectric particles embedded in the middle layer. Such geometries are typical of…
A family of mixed finite elements is proposed for solving the first order system of linear elasticity equations in any space dimension, where the stress field is approximated by symmetric finite element tensors. This family of elements has…
We propose and explore a new, general-purpose method for the implicit time integration of elastica. Key to our approach is the use of a mixed variational principle. In turn its finite element discretization leads to an efficient alternating…
We consider an equation modeling the evolution of a viscous liquid thin film wetting a horizontal solid substrate destabilized by an electric field normal to the substrate. The effects of the electric field are modeled by a lower order…
We study exact solutions of nonlinear electrodynamics coupled to three-dimensional gravity with torsion. We show that in any static and spherically symmetric configuration, at least one component of the electromagnetic field has to vanish.…
We present a numerical method for the solution of linear magnetostatic problems in domains with a symmetry direction, including axial and translational symmetry. The approach uses a Fourier series decomposition of the vector potential…
Piezoelectric appliances have become hugely important in the past century and computer simulations play an essential part in the modern design process thereof. While much work has been invested into the practical simulation of piezoelectric…
Employing a limiting case of a conjecture for constructing piecewise separable-variables functions, the elements of the Pseudoanalytic Function Theory are used for numerically approaching solutions of the forward Dirichlet boundary value…
The present article proposes a partitioned Dirichlet-Neumann algorithm, that allows to address unique challenges arising from a novel mixed-dimensional coupling of very slender fibers embedded in fluid flow using a regularized mortar-type…
A dynamic linear thermo-poroelasticity model, containing inertial and relaxation terms with second-order time derivatives, is investigated in this paper. The mathematical and numerical analysis of this model is performed in the frequency…
We consider a variational model for magnetoelastic solids in the large-strain setting with the magnetization field defined on the unknown deformed configuration. Through a simultaneous linearization of the deformation and sharp-interface…
Simulating electromagnetic fields across broad frequency ranges is challenging due to numerical instabilities at low frequencies. This work extends a stabilized two-step formulation of Maxwell's equations to the time-domain. Using a…
In the present study we investigate electrostatic stabilization mechanisms acting on stratified fluids. Electric fields have been shown to control and even suppress the Rayleigh-Taylor instability when a heavy fluid lies above lighter…
We study the three-dimensional compressible elastic Navier-Stokes-Poisson equations induced by a new bipolar viscoelastic model derived here, which model the motion of the compressible electrically conducting fluids. The various boundary…
In this paper, new unfitted mixed finite elements are presented for elliptic interface problems with jump coefficients. Our model is based on a fictitious domain formulation with distributed Lagrange multiplier. The relevance of our…
This work presents a modified domain integral equation approach for the forward problem of TE scattering, employing a modified definition of dielectric contrast and discretizing the electric field density using Rao-Wilton-Glisson (RWG)…
The aim of this article is to study a nonlinear system modeling a Non-Newtonian fluid of polymer aqueous solutions. We are interested here in the existence of weak solutions for the stationary problem in a bounded plane domain or in…
We present a scalable, parallel implementation of a solver for the solution of a phase-field model for quasi-static brittle fracture. The code is available as open source. Numerical solutions in 2d and 3d with adaptive mesh refinement show…
We study frequency domain electromagnetic scattering at a bounded, penetrable, and inhomogeneous obstacle $ \Omega \subset \mathbb{R}^3 $. From the Stratton-Chu integral representation, we derive a new representation formula when constant…