Related papers: Simultaneous Analysis of Continuously Embedded Rei…
We compare convergence of isogeometric analysis (IGA), a spline modification of finite element method (FEM), with FEM in the context of our real space code for ab-initio electronic structure calculations of non-periodic systems. The…
In this communication the advantages and drawbacks of the isogeometric analysis (IGA) are reviewed in the context of electromagnetic simulations. IGA extends the set of polynomial basis functions, commonly employed by the classical Finite…
A methodology for determining the scattered Electromagnetic (EM) fields present for interconnected regions with common metasurface boundaries is presented. The method uses a Boundary Element Method (BEM) formulation of the frequency domain…
A Trace-Finite-Cell-Method for the numerical analysis of thin shells is presented combining concepts of the TraceFEM and the Finite-Cell-Method. As an underlying shell model we use the Koiter model, which we re-derive in strong form based…
We discuss the efficient implementation of a high-performance second-order collocation-type finite-element scheme for solving the compressible Euler equations of gas dynamics on unstructured meshes. The solver is based on the convex…
In this work, we report a massively parallel and time domain implementation of the 3D phase field model that can reach beyond micron scale and consider for arbitrary electrical and mechanical boundary conditions. The first part of the paper…
In this work, we present a boundary and hole detection approach that traverses all the boundaries of an edge-manifold triangular mesh, irrespectively of the presence of singular vertices, and subsequently determines and labels all holes of…
Fluid-Structure Interaction (FSI) can be investigated by means of non-linear Finite Element Models (FEM), suitable to capture large deflections of structural parts interacting with fluids, and Computational Fluid Dynamics (CFD). High…
The presented paper concentrates on the boundary element method (BEM) for the heat equation in three spatial dimensions. In particular, we deal with tensor product space-time meshes allowing for quadrature schemes analytic in time and…
The Poisson equation governing a planet's gravitational field is posed on the unbounded domain, $\mathbb{R}^3$, whereas finite-element computations require bounded meshes. We implement and compare three strategies for handling the infinite…
Spectral element methods (SEM), which are extensions of finite element methods (FEM), are important emerging techniques for solving partial differential equations in physics and engineering. SEM can potentially deliver better accuracy due…
We develop an all-hex meshing strategy for the interstitial space in beds of densely packed spheres that is tailored to turbulent flow simulations based on the spectral element method (SEM). The SEM achieves resolution through elevated…
In this paper the numerical solution of potential problems defined on 3D unbounded domains is addressed with Boundary Element Methods (BEMs), since in this way the problem is studied only on the boundary, and thus any finite approximation…
This work presents a Boundary Element Method (BEM) formulation for contactless electromagnetic field assessments. The new scheme is based on a regularized BEM approach that requires the use of electric measurements only. The regularization…
We present a convergence result for the finite volume method applied to a particular phase field problem suitable for simulation of pure substance solidification. The model consists of the heat equation and the phase field equation with a…
A Nitche's method is presented to couple different mechanical models. They include coupling of a solid and a beam and of a solid and a plate. Both conforming and non-conforming formulations are presented. In a non-conforming for- mulation,…
The $h$-version of the finite-element method ($h$-FEM) applied to the high-frequency Helmholtz equation has been a classic topic in numerical analysis since the 1990s. It is now rigorously understood that (using piecewise polynomials of…
In this work, we propose the application of the eXtended Finite Element Method (XFEM) in the context of the coupling between three-dimensional and one-dimensional elliptic problems. In particular, we consider the case in which the 3D-1D…
Metasurfaces have become a promising means for manipulating optical wavefronts in flat and high-performance optical devices. Conventional metasurface device design relies on trial-and-error methods to obtain target electromagnetic (EM)…
This work describes models and numerical approximations that describe the mechanical behavior of deformable continua with embedded structural members, such as rigid bodies, beams, shells, etc. The continuum formulation extends an idea first…