相关论文: Residual stresses in metal deposition modeling: di…
The multi-level hp-refinement scheme is a powerful extension of the finite element method that allows local mesh adaptation without the trouble of constraining hanging nodes. This is achieved through hierarchical high-order overlay meshes,…
This contribution presents a hierarchical multigrid approach for the solution of large-scale finite cell problems on both uniform grids and multi-level hp-discretizations. The proposed scheme leverages the hierarchical nature of the basis…
The finite cell method is a highly flexible discretization technique for numerical analysis on domains with complex geometries. By using a non-boundary conforming computational domain that can be easily meshed, automatized computations on a…
In the present work, we investigate the computational efficiency afforded by higher-order finite-element discretization of the saddle-point formulation of orbital-free density functional theory. We first investigate the robustness of viable…
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…
We present a new high order finite element method for the discretization of partial differential equations on stationary smooth surfaces which are implicitly described as the zero level of a level set function. The discretization is based…
We extend a localized model order reduction method for the distributed finite element solution of elliptic boundary value problems in the cloud. We give a computationally efficient technique to compute the required inner product matrices…
We present a novel framework for PDE-constrained $r$-adaptivity of high-order meshes. The proposed method formulates mesh movement as an optimization problem, with an objective function defined as a convex combination of a mesh quality…
We propose a class of temporally high-order parametric finite element methods for simulating solid-state dewetting of thin films in two dimensions using a sharp-interface model. The process is governed by surface diffusion and contact point…
In this work, we propose a novel formulation for the solution of partial differential equations using finite element methods on unfitted meshes. The proposed formulation relies on the discrete extension operator proposed in the aggregated…
Efficient exploitation of exascale architectures requires rethinking of the numerical algorithms used in many large-scale applications. These architectures favor algorithms that expose ultra fine-grain parallelism and maximize the ratio of…
The Finite Element Method (FEM) is the gold standard for spatial discretization in numerical simulations for a wide spectrum of real-world engineering problems. Prototypical areas of interest include linear heat transfer and linear…
The finite-element method is a preferred numerical method when electromagnetic fields at high accuracy are to be computed in nano-optics design. Here, we demonstrate a finite-element method using hp-adaptivity on tetrahedral meshes for…
A simple method for improving cache efficiency of serial and parallel explicit finite procedure with application to casting solidification simulation over three-dimensional complex geometries is presented. The method is based on division of…
We present a new framework for expressing finite element methods on multiple intersecting meshes: multimesh finite element methods. The framework enables the use of separate meshes to discretize parts of a computational domain that are…
In this work we propose and analyze a novel Hybrid High-Order discretization of a class of (linear and) nonlinear elasticity models in the small deformation regime which are of common use in solid mechanics. The proposed method is valid in…
When modeling scientific and industrial problems, geometries are typically modeled by explicit boundary representations obtained from computer-aided design software. Unfitted (also known as embedded or immersed) finite element methods offer…
In this contribution we investigate in mathematical modeling and efficient simulation of biological cells with a particular emphasis on effective modeling of structural properties that originate from active forces generated from…
In this paper a class of higher order finite element methods for the discretization of surface Stokes equations is studied. These methods are based on an unfitted finite element approach in which standard Taylor-Hood spaces on an underlying…
The finite element method can be viewed as a machine that automates the discretization of differential equations, taking as input a variational problem, a finite element and a mesh, and producing as output a system of discrete equations.…