Related papers: Elemental matrices for the finite element method i…
In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…
The capability of discretization of matrix elements in the problem of quadratic functional minimization with linear member built on matrix in N-dimensional configuration space with discrete coordinates is researched. It is shown, that…
A precise domain triangulation is recognized as indispensable for the accurate numerical approximation of differential operators within collocation methods, leading to a substantial reduction in discretization errors. An efficient finite…
This paper introduces an accurate edge-based smoothed finite element method (ES-FEM) for electromagnetic analysis for both two dimensional cylindrical and three dimensional cartesian systems, which shows much better performance in terms of…
We present a broad family of high-order finite element algorithms for simulating the flow of electroneutral electrolytes. The governing partial differential equations that we solve are the electroneutral…
This is a study of certain finite element methods designed for convection-dominated, time-dependent partial differential equations. Specifically, we analyze high order space-time tensor product finite element discretizations, used in a…
This lecture note describes how to set up and what is behind a magnetodynamic field simulation for an accelerator magnet. The relevant formulation of Maxwell's equations is derived. The formulation is discretized in space by the…
In this paper, we present a finite element method (FEM) framework enhanced by an operator-adapted wavelet decomposition algorithm designed for the efficient analysis of multiscale electromagnetic problems. Usual adaptive FEM approaches,…
The aim of this paper is to establish convergence, properties and error bounds for the fully discrete solutions of a class of nonlinear systems of reaction-diffusion nonlocal type with moving boundaries, using the finite element method with…
We present quantitative means for assessing the numerical accuracy of static magnetic field calculations in finite-element models. Our calculations use the three-dimensional Opera simulation software suite of Dassault Syst`emes. Our need to…
The finite element analysis of high frequency vibrations of quartz crystal plates is a necessary process required in the design of quartz crystal resonators of precision types for applications in filters and sensors. The anisotropic…
In this paper we describe a methodology for the identification of symmetric quadrature rules inside of quadrilaterals, triangles, tetrahedra, prisms, pyramids, and hexahedra. The methodology is free from manual intervention and is capable…
Using a complete basis set we have obtained an analytic expression for the matrix elements of the Coulomb interaction. These matrix elements are written in a closed form. We have used the basis set of the three-dimensional isotropic quantum…
We develop a new spatial semidiscrete multiscale method based upon the edge multiscale methods to solve semilinear parabolic problems with heterogeneous coefficients and smooth initial data. This method allows for a cheap spatial…
A nonlinear analysis of high-frequency thickness-shear vibrations of AT-cut quartz crystal plates is presented with the two-dimensional finite element method. We expanded both kinematic and constitutive nonlinear Mindlin plate equations and…
We discuss a class of magnetic-electric fields based finite element schemes for stationary magnetohydrodynamics (MHD) systems with two types of boundary conditions. We establish a key $L^{3}$ estimate for divergence-free finite element…
This work describes a concise algorithm for the generation of triangular meshes with the help of standard adaptive finite element methods. We demonstrate that a generic adaptive finite element solver can be repurposed into a triangular mesh…
Mesh adaption procedures for finite element approximation allows one to adapt the resolution, by local refinement in the regions of strong variation of the function of interest. This procedure plays a key role in numerous applications of…
We present rigorous 3D EMF simulations of isolated features on photomasks using a newly developed finite-element method. We report on the current status of the finite-element solver JCMsuite, incorporating higher-order edge elements,…
The finite element method (FEM) is a cornerstone numerical technique for solving partial differential equations (PDEs). Here, we present $\textbf{Qu-FEM}$, a fault-tolerant era quantum algorithm for the finite element method. In contrast to…