Related papers: Benchmark of Polygon Quality Metrics for Polytopal…
We introduce the harmonic virtual element method (harmonic VEM), a modification of the virtual element method (VEM) for the approximation of the 2D Laplace equation using polygonal meshes. The main difference between the harmonic VEM and…
A virtual element method (VEM) with the first order optimal convergence order is developed for solving two-dimensional Maxwell interface problems on a special class of polygonal meshes that are cut by the interface from a background…
In this paper we analyze a virtual element method for the two dimensional elasticity problem allowing small edges. With this approach, the classic assumptions on the geometrical features of the polygonal meshes can be relaxed. In…
Three different displacement based finite element formulations over arbitrary polygons are studied in this paper. The formulations considered are: the conventional polygonal finite element method (FEM) with Laplace interpolants, the…
A novel multi-scale finite element formulation for contact mechanics between nominally smooth but microscopically rough surfaces is herein proposed. The approach integrates the interface finite element method (FEM) for modelling interface…
Some methods based on simple regularizing geometric element transformations have heuristically been shown to give runtime efficient and quality effective smoothing algorithms for meshes. We describe the mathematical framework and a…
We propose a quality-based optimization strategy to reduce the total number of degrees of freedom associated to a discrete problem defined over a polygonal tessellation with the Virtual Element Method. The presented Quality Agglomeration…
In this letter we compare the behaviour of standard Virtual Element Methods (VEM) and stabilization free Enlarged Enhancement Virtual Element Methods (E$^2$VEM) with the focus on some elliptic test problems whose solution and diffusivity…
The Finite Element Method (FEM) is a powerful computational tool for solving partial differential equations (PDEs). Although commercial and open-source FEM software packages are widely available, an independent implementation of FEM…
Finite element methods are well-known to admit robust optimal convergence on simplicial meshes satisfying the maximum angle conditions. But how to generalize this condition to polyhedra is unknown in the literature. In this work, we argue…
Synthetic polymeric materials underpin fundamental technologies in the energy, electronics, consumer goods, and medical sectors, yet their development still suffers from prolonged design timelines. Although polymer informatics tools have…
One of the major issues in the computational mechanics is to take into account the geometrical complexity. To overcome this difficulty and to avoid the expensive mesh generation, geometrically unfitted methods, i.e. the numerical methods…
In the present thesis, a computational framework for the analysis of the deformation and damage phenomena occurring at the micro-scale of polycrystalline materials is presented. Micro-mechanics studies are commonly performed using the…
The virtual element method (VEM) is a stabilized Galerkin method that is robust and accurate on general polygonal meshes. This feature makes it an appealing candidate for simulations involving meshes with embedded interfaces and evolving…
This paper addresses the problem of evaluating the quality of finite element meshes for the purpose of structural mechanic simulations. It proposes the application of a machine learning model trained on data collected from expert…
In this work we compare crucial parameters for efficiency of different finite element methods for solving partial differential equations (PDEs) on polytopal meshes. We consider the Virtual Element Method (VEM) and different Discontinuous…
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…
This paper introduces a new weak Galerkin (WG) finite element method for second order elliptic equations on polytopal meshes. This method, called WG-FEM, is designed by using a discrete weak gradient operator applied to discontinuous…
In this paper, we use the first-order virtual element method (VEM) to investigate the effect of shape quality of polyhedra in the estimation of the critical time step for explicit three-dimensional elastodynamic finite element (FE)…
The Virtual Element Method (VEM) is a well-established framework for solving partial differential equations on polygonal and polyhedral meshes. In this paper, we introduce a novel hybrid VEM that integrates both conforming and nonconforming…