Related papers: Finite-element based electromagnetic field simulat…
Error estimates are proved for finite element approximations to the solution of second-order hyperbolic partial differential equations with coefficients varying in both space and time. Optimal rates of convergence in the energy norm are…
This document gives guidelines to set up, run, and postprocess correct simulations with the finite element method. It is not an introduction to the method itself, but rather a list of things to check and possible mistakes to watch out for…
The numerical analysis for the small amplitude motion of an elastic beam with internal damping is investigated in domain with moving ends. An efficient numerical method is constructed to solve this moving boundary problem. The stability and…
The paper presents a numerical study for the finite element method with anisotropic meshes. We compare the accuracy of the numerical solutions on quasi-uniform, isotropic, and anisotropic meshes for a test problem which combines several…
We suggest a finite element method for computing minimal surfaces based on computing a discrete Laplace-Beltrami operator operating on the coordinates of the surface. The surface is a discrete representation of the zero level set of a…
We introduce a new formulation for the finite element immersed boundary method which makes use of a distributed Lagrange multiplier. We prove that a full discretization of our model, based on a semi-implicit time advancing scheme, is…
We demonstrate the interest of combining Finite Element calculations with the Vector Partial Wave formulation (used in T-matrix and Mie theory) in order to characterize the electromagnetic scattering properties of isolated individual…
In this paper, a symmetrized two-scale finite element method is proposed for a class of partial differential equations with symmetric solutions. With this method, the finite element approximation on a fine tensor product grid is reduced to…
Interpolation methods for nonlinear finite element discretizations are commonly used to eliminate the computational costs associated with the repeated assembly of the nonlinear systems. While the group finite element formulation…
Interferometric scattering microscopy is a powerful technique that enables various applications, such as mass photometry and particle tracking. Here we present a numerical toolbox to simulate images obtained in interferometric scattering,…
The numerical solution of a nonlinear and space-fractional anti-diffusive equation used to model dune morphodynamics is considered. Spatial discretization is effected using a finite element method whereas the Crank-Nicolson scheme is used…
The purpose of this paper is to investigate the scattering by a nonlinear crystal whose depth is about the wavelength of the impinging field. More precisely, an infinite nonlinear slab is illuminated by an incident field which is the sum of…
We propose a method for optical nano-imaging in which the structure of a three-dimensional inhomogeneous medium may be recovered from far-field power measurements. Neither phase control of the illuminating field nor phase measurements of…
Interfacial energy plays an important role in equilibrium morphologies of nanosized microstructures of solid materials due to the high interface-to-volume ratio, and can no longer be neglected as it does in conventional mechanics analysis.…
Using the Green's dyad technique based on cuboidal meshing, we compute the electromagnetic field scattered by metal nanorods with high aspect ratio. We investigate the effect of the meshing shape on the numerical simulations. We observe…
Mixed finite element methods are considered for a ferrofluid flow model with magnetization paralleled to the magnetic field. The ferrofluid model is a coupled system of the Maxwell equations and the incompressible Navier-Stokes equations.…
The paper introduces a finite element method for the incompressible Navier--Stokes equations posed on a closed surface $\Gamma\subset\R^3$. The method needs a shape regular tetrahedra mesh in $\mathbb{R}^3$ to discretize equations on the…
We present Fiend - a simulation package for three-dimensional single-particle time-dependent Schr\"odinger equation for cylindrically symmetric systems. Fiend has been designed for the simulation of electron dynamics under inhomogeneus…
A fast and stable numerical method is formulated to compute the time evolution of a wave function in a magnetic field by solving the time-dependent Schroedinger equation. This computational method is based on the finite element method in…
Finite element model updating of a structure made of linear elastic materials is based on the solution of a minimization problem. The goal is to find some unknown parameters of the finite element model (elastic moduli, mass densities,…