48 research outputs found
Mini-Workshop: Numerical Upscaling for Flow Problems: Theory and Applications
The objective of this workshop was to bring together researchers working in multiscale simulations with emphasis on multigrid methods and multiscale finite element methods, aiming at chieving of better understanding and synergy between these methods. The goal of multiscale finite element methods, as upscaling methods, is to compute coarse scale solutions of the underlying equations as accurately as possible. On the other hand, multigrid methods attempt to solve fine-scale equations rapidly using a hierarchy of coarse spaces. Multigrid methods need “good” coarse scale spaces for their efficiency. The discussions of this workshop partly focused on approximation properties of coarse scale spaces and multigrid convergence. Some other presentations were on upscaling, domain decomposition methods and nonlinear multiscale methods. Some researchers discussed applications of these methods to reservoir simulations, as well as to simulations of filtration, insulating materials, and turbulence
Truncation preconditioners for stochastic Galerkin finite element discretizations
Stochastic Galerkin finite element method (SGFEM) provides an efficient
alternative to traditional sampling methods for the numerical solution of
linear elliptic partial differential equations with parametric or random
inputs. However, computing stochastic Galerkin approximations for a given
problem requires the solution of large coupled systems of linear equations.
Therefore, an effective and bespoke iterative solver is a key ingredient of any
SGFEM implementation. In this paper, we analyze a class of truncation
preconditioners for SGFEM. Extending the idea of the mean-based preconditioner,
these preconditioners capture additional significant components of the
stochastic Galerkin matrix. Focusing on the parametric diffusion equation as a
model problem and assuming affine-parametric representation of the diffusion
coefficient, we perform spectral analysis of the preconditioned matrices and
establish optimality of truncation preconditioners with respect to SGFEM
discretization parameters. Furthermore, we report the results of numerical
experiments for model diffusion problems with affine and non-affine parametric
representations of the coefficient. In particular, we look at the efficiency of
the solver (in terms of iteration counts for solving the underlying linear
systems) and compare truncation preconditioners with other existing
preconditioners for stochastic Galerkin matrices, such as the mean-based and
the Kronecker product ones.Comment: 27 pages, 6 table
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