Related papers: Refinement strategies for polygonal meshes applied…
This paper presents the Virtual Element Method (VEM) for the modeling of crack propagation in 2D within the context of linear elastic fracture mechanics (LEFM). By exploiting the advantage of mesh flexibility in the VEM, we establish an…
The discrete element method (DEM) is a powerful tool for simulating granular soils, but its high computational demand often results in extended simulation times. While the effect of particle size has been extensively studied, the potential…
As modeling and visualization applications proliferate, there arises a need to simplify large polygonal models at interactive rates. Unfortunately existing polygon mesh simplification algorithms are not well suited for this task because…
We present an improved method for topology optimization with both adaptive mesh refinement and derefinement. Since the total volume fraction in topology optimization is usually modest, after a few initial iterations the domain of…
We develop a sparse multiscale operator-adapted wavelet decomposition-based finite element method (FEM) on unstructured polygonal mesh hierarchies obtained via a coarsening procedure. Our approach decouples different resolution levels,…
Nowadays, several models of unidimensional fluid jets exploit discrete element methods. In some cases, as for models aiming at describing the electrospinning nanofabrication process of polymer fibers, discrete element methods suffer a non…
Many problems in science and engineering can be rigorously recast into minimizing a suitable energy functional. We have been developing efficient and flexible solution strategies to tackle various minimization problems by employing finite…
Polytopal Element Methods (PEM) allow to solve differential equations on general polygonal and polyhedral grids, potentially offering great flexibility to mesh generation algorithms. Differently from classical finite element methods, where…
This contribution introduces the idea of refinement patterns for the generation of optimal meshes in the context of the Finite Element Method. The main idea is to generate a library of possible patterns on which elements can be refined and…
Topological optimization finds a material density distribution minimizing a functional of the solution of a partial differential equation (PDE), subject to a set of constraints (typically, a bound on the volume or mass of the material).…
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…
It is well known that the quasi-optimality of the Galerkin finite element method for the Helmholtz equation is dependent on the mesh size and the wave-number. In the literature, different criteria have been proposed to ensure uniform…
We present the design and implementation details of a geometric multigrid method on adaptively refined meshes for massively parallel computations. The method uses local smoothing on the refined part of the mesh. Partitioning is achieved by…
We present a new discretization method for homogeneous convection-diffusion-reaction boundary value problems in 3D that is a non-standard finite element method with PDE-harmonic shape functions on polyhedral elements. The element stiffness…
In this paper we develop adaptive numerical schemes for certain nonlinear variational problems. The discretization of the variational problems is done by representing the solution as a suitable frame decomposition, i.e., a complete, stable,…
An adaptive isogeometric method based on $d$-variate hierarchical spline constructions can be derived by considering a refine module that preserves a certain class of admissibility between two consecutive steps of the adaptive loop [6]. In…
Adaptive meshing is a fundamental component of adaptive finite element methods. This includes refining and coarsening meshes locally. In this work, we are concerned with the red-green-blue refinement strategy in two dimensions and its…
We explore the recently-proposed Virtual Element Method (VEM) for numerical solution of boundary value problems on arbitrary polyhedral meshes. More specifically, we focus on the elasticity equations in three-dimensions and elaborate upon…
Monotone finite difference methods provide stable convergent discretizations of a class of degenerate elliptic and parabolic Partial Differential Equations (PDEs). These methods are best suited to regular rectangular grids, which leads to…
We adapt the Gradient Discretisation Method (GDM), originally designed for elliptic and parabolic partial differential equations, to the case of a linear scalar hyperbolic equations. This enables the simultaneous design and convergence…