546 research outputs found
Computational Engineering
The focus of this Computational Engineering Workshop was on the mathematical foundation of state-of-the-art and emerging finite element methods in engineering analysis. The 52 participants included mathematicians and engineers with shared interest on discontinuous Galerkin or Petrov-Galerkin methods and other generalized nonconforming or mixed finite element methods
SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES
Crack propagation in thin shell structures due to cutting is conveniently simulated
using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell
elements are usually preferred for the discretization in the presence of complex material
behavior and degradation phenomena such as delamination, since they allow for a correct
representation of the thickness geometry. However, in solid-shell elements the small thickness
leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new
selective mass scaling technique is proposed to increase the time-step size without affecting
accuracy. New ”directional” cohesive interface elements are used in conjunction with selective
mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile
shells
Self-Adaptive Methods for PDE
[no abstract available
HDGlab: An Open-Source Implementation of the Hybridisable Discontinuous Galerkin Method in MATLAB
This paper presents HDGlab, an open source MATLAB implementation of the hybridisable discontinuous Galerkin (HDG) method. The main goal is to provide a detailed description of both the HDG method for elliptic problems and its implementation available in HDGlab. Ultimately, this is expected to make this relatively new advanced discretisation method more accessible to the computational engineering community. HDGlab presents some features not available in other implementations of the HDG method that can be found in the free domain. First, it implements high-order polynomial shape functions up to degree nine, with both equally-spaced and Fekete nodal distributions. Second, it supports curved isoparametric simplicial elements in two and three dimensions. Third, it supports non-uniform degree polynomial approximations and it provides a flexible structure to devise degree adaptivity strategies. Finally, an interface with the open-source high-order mesh generator Gmsh is provided to facilitate its application to practical engineering problems
High-order Discontinuous Galerkin methods for the elastodynamics equation on polygonal and polyhedral meshes
We propose and analyze a high-order Discontinuous Galerkin Finite Element Method for the approximate solution of wave propagation problems modeled by the elastodynamics equations on computational meshes made by polygonal and polyhedral elements. We analyze the well posedness of the resulting formulation, prove hp-version error a-priori estimates, and present a dispersion analysis, showing that polygonal meshes behave as classical simplicial/quadrilateral grids in terms of dispersion properties. The theoretical estimates are confirmed through various two-dimensional numerical verifications
A space-time discontinuous Galerkin method for coupled poroelasticity-elasticity problems
This work is concerned with the analysis of a space-time finite element
discontinuous Galerkin method on polytopal meshes (XT-PolydG) for the numerical
discretization of wave propagation in coupled poroelastic-elastic media. The
mathematical model consists of the low-frequency Biot's equations in the
poroelastic medium and the elastodynamics equation for the elastic one. To
realize the coupling, suitable transmission conditions on the interface between
the two domains are (weakly) embedded in the formulation. The proposed PolydG
discretization in space is then coupled with a dG time integration scheme,
resulting in a full space-time dG discretization. We present the stability
analysis for both the continuous and the semidiscrete formulations, and we
derive error estimates for the semidiscrete formulation in a suitable energy
norm. The method is applied to a wide set of numerical test cases to verify the
theoretical bounds. Examples of physical interest are also presented to
investigate the capability of the proposed method in relevant geophysical
scenarios
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