Related papers: Finite element based Green's function integral equ…
In this paper we introduce a new class of finite element discretizations of the quadratic optimal transport problem based on its dynamical formulation. These generalize to the finite element setting the finite difference scheme proposed by…
We present an integral equation-based method for the numerical solution of two-point boundary value systems. Special care is devoted to the mathematical formulation, namely the choice of the background Green's function that leads to a…
We investigate the influence of a time dependent, homogeneous electric field on scattering properties of non-interacting electrons in an arbitrary static potential. We develop a method to calculate the (Keldysh) Green's function in two…
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…
A self-contained discussion of integral equations of scattering is presented in the case of centrally-symmetric potentials in one dimension, which will facilitate the understanding of more complex scattering integral equations in two and…
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,…
A proof of convergence is given for semi- and full discretizations of mean curvature flow of closed two-dimensional surfaces. The numerical method proposed and studied here combines evolving finite elements, whose nodes determine the…
Korringa-Kohn-Rostoker (KKR) Green's function, multiple-scattering theory is an efficient site-centered, electronic-structure technique for addressing an assembly of $N$ scatterers. Wave-functions are expanded in a spherical-wave basis on…
An error control technique aimed to assess the quality of smoothed finite element approximations is presented in this paper. Finite element techniques based on strain smoothing appeared in 2007 were shown to provide significant advantages…
We consider a sketched implementation of the finite element method for elliptic partial differential equations on high-dimensional models. Motivated by applications in real-time simulation and prediction we propose an algorithm that…
We use a finite-element method to obtain highly converged results for a nano-optical light scattering setup with a non-periodic geometry.
A general approach for the calculation of the incoherent intensity scattered by a random medium with rough boundaries has been developed using a Green function formalism. The random medium consists of spherical particles whose physical…
In this technical report, we present estimations of the discrete Green's function of the streamline diffusion finite element method (SDFEM) on Shishkin triangular meshes for problems with only exponential layers.
This paper presents a full-spectrum Green function methodology (which is valid, in particular, at and around Wood-anomaly frequencies) for evaluation of scattering by periodic arrays of cylinders of arbitrary cross section-with application…
We present a new boundary integral formulation for time-harmonic wave diffraction from two-dimensional structures with many layers of arbitrary periodic shape, such as multilayer dielectric gratings in TM polarization. Our scheme is robust…
This paper is devoted to show a discrete adaptive finite element approximation result for the isotropic two-dimensional Griffith energy arising in fracture mechanics. The problem is addressed in the geometric measure theoretic framework of…
This paper analyses the finite element component of the error when using preintegration to approximate the cdf and pdf for uncertainty quantification (UQ) problems involving elliptic PDEs with random inputs. It is a follow up to Gilbert,…
Geometric particle-in-cell discretizations have been derived based on a discretization of the fields that is conforming with the de Rham structure of the Maxwell's equation and a standard particle-in-cell ansatz for the fields by deriving…
Methods for solving Maxwell's equations are integral part of optical metrology and computational lithography setups. Applications require accurate geometrical resolution, high numerical accuracy and/or low computation times. We present a…
We consider numerical simulation of the isotropic elastic wave equations arising from seismic applications with non-trivial land topography. The more flexible finite element method is applied to the shallow region of the simulation domain…