2,275 research outputs found
Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods
In this paper, we discuss a general multiscale model reduction framework
based on multiscale finite element methods. We give a brief overview of related
multiscale methods. Due to page limitations, the overview focuses on a few
related methods and is not intended to be comprehensive. We present a general
adaptive multiscale model reduction framework, the Generalized Multiscale
Finite Element Method. Besides the method's basic outline, we discuss some
important ingredients needed for the method's success. We also discuss several
applications. The proposed method allows performing local model reduction in
the presence of high contrast and no scale separation
Revisiting topology optimization with buckling constraints
We review some features of topology optimization with a lower bound on the
critical load factor, as computed by linearized buckling analysis. The change
of the optimized design, the competition between stiffness and stability
requirements and the activation of several buckling modes, depending on the
value of such lower bound, are studied. We also discuss some specific issues
which are of particular interest for this problem, as the use of non-conforming
finite elements for the analysis, the use of inconsistent sensitivities in the
optimization and the replacement of the single eigenvalue constraints with an
aggregated measure. We discuss the influence of these practices on the
optimization result, giving some recommendations.Comment: 15 pages, 12 figures, 2 table
A p-multigrid method enhanced with an ILUT smoother and its comparison to h-multigrid methods within Isogeometric Analysis
Over the years, Isogeometric Analysis has shown to be a successful
alternative to the Finite Element Method (FEM). However, solving the resulting
linear systems of equations efficiently remains a challenging task. In this
paper, we consider a p-multigrid method, in which coarsening is applied in the
approximation order p instead of the mesh width h. Since the use of classical
smoothers (e.g. Gauss-Seidel) results in a p-multigrid method with
deteriorating performance for higher values of p, the use of an ILUT smoother
is investigated. Numerical results and a spectral analysis indicate that the
resulting p-multigrid method exhibits convergence rates independent of h and p.
In particular, we compare both coarsening strategies (e.g. coarsening in h or
p) adopting both smoothers for a variety of two and threedimensional
benchmarks
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