Related papers: A mixed-dimensional model for the electrostatic pr…
We derive a variational formulation for thin film magnetization problems in type-II superconductors written in terms of two variables, the electric field and the magnetization function. A numerical method, based on this formulation, makes…
We present the mathematical theory and its numerical validation of a method tailored to include eddy-current effects only in a part of the domain. This results in a heterogeneous problem combining an eddy-current model in a subset of the…
We investigate the two-dimensional elastostatic inclusion problem in an unbounded medium. Building on the recent developments for rigid inclusions \cite{Mattei:2021:EAS} and conductivity inclusions \cite{Jung:2021:SEL}, we extend these…
The finite-element analysis of three-dimensional magnetostatic problems in terms of magnetic vector potential has proven to be one of the most efficient tools capable of providing the excellent quality results but becoming computationally…
In article the following tasks on computer modeling of electric fields are analyzed: 1) calculation of distribution of potential for the field created by two parallel plates and charged bodies in the non-uniform environment; 2) calculation…
We consider a set of electrostatic problems relevant for determining the real-space structure and the ground-state energy of a two-dimensional electron liquid subject to smooth external potentials. Three fundamental geometries are…
A direct numerical simulation of the three-dimensional elektrokinetic instability near a charge selective surface (electric membrane, electrode, or system of micro-/nanochannels) is carried out and analyzed. A special finite-difference…
This article presents a general approach akin to domain-decomposition methods to solve a single linear PDE, but where each subdomain of a partitioned domain is associated to a distinct variational formulation coming from a mutually…
We construct a finite element approximation of a strain-limiting elastic model on a bounded open domain in $\mathbb{R}^d$, $d \in \{2,3\}$. The sequence of finite element approximations is shown to exhibit strong convergence to the unique…
Three dimensional field configuration has been simulated for a simple wire chamber consisting of one anode wire stretched along the axis of a grounded square cathode tube by solving numerically the boundary integral equation of the first…
We simulate the electrical response of multiple disjoint biological 3D cells undergoing an electropermeabilization process. Instead of solving the boundary value problem in the unbounded volume, we reduce it to a system of boundary…
Rigorous computer simulations of propagating electromagnetic fields have become an important tool for optical metrology and design of nanostructured optical components. A vectorial finite element method (FEM) is a good choice for an…
The finite element method is one of the widely employed numerical techniques in electrical engineering for the study of electric and magnetic fields. When applied to the moving conductor problems, the finite element method is known to have…
We consider the dynamics of an electrostatically actuated thin elastic plate being clamped at its boundary above a rigid plate. The model includes the harmonic electrostatic potential in the three-dimensional time-varying region between the…
We consider an elliptic partial differential equation in non-divergence form with a random diffusion matrix and random forcing term. To address this, we propose a mixed-type continuous finite element discretization in the physical domain,…
We present an elastic simulator for domains defined as evolving implicit functions, which is efficient, robust, and differentiable with respect to both shape and material. This simulator is motivated by applications in 3D reconstruction: it…
This paper is devoted to the study of a novel mixed Finite Element Method for approximating the solutions of fourth order variational problems subjected to a constraint. The first problem we consider consists in establishing the convergence…
The state of art of time domain integral equation (TDIE) solvers has grown by leaps and bounds over the past decade. During this time, advances have been made in (i) the development of accelerators that can be retrofitted with these solvers…
This note deals with a tearing and interconnecting (special non-overlapping domain decomposition) formulation for magneto-quasi-statics (also known as the eddy current model). Only two subdomains are considered, one conducting and one…
This paper is concerned with the Boundary Element simulation of elastic domains that contain thin inclusions that have elastic material properties, which are different to the domain. With thin inclusions we mean inclusions with extreme…