145 research outputs found
Strict lower bounds with separation of sources of error in non-overlapping domain decomposition methods
This article deals with the computation of guaranteed lower bounds of the
error in the framework of finite element (FE) and domain decomposition (DD)
methods. In addition to a fully parallel computation, the proposed lower bounds
separate the algebraic error (due to the use of a DD iterative solver) from the
discretization error (due to the FE), which enables the steering of the
iterative solver by the discretization error. These lower bounds are also used
to improve the goal-oriented error estimation in a substructured context.
Assessments on 2D static linear mechanic problems illustrate the relevance of
the separation of sources of error and the lower bounds' independence from the
substructuring. We also steer the iterative solver by an objective of precision
on a quantity of interest. This strategy consists in a sequence of solvings and
takes advantage of adaptive remeshing and recycling of search directions.Comment: International Journal for Numerical Methods in Engineering, Wiley,
201
Solvendo est dominium
Seminar at TU MunchenThis presentation was given for the 50th birthday of the department of applied mechanics of the Technical University of Munich (Germany)Présentation donnée pour le 50eme anniversaire du département de mécanique appliquée de l'Université Technologique de Munich (Allemagne
Virtual Delamination Testing through Non-Linear Multi-Scale Computational Methods: Some Recent Progress
This paper deals with the parallel simulation of delamination problems at the
meso-scale by means of multi-scale methods, the aim being the Virtual
Delamination Testing of Composite parts. In the non-linear context, Domain
Decomposition Methods are mainly used as a solver for the tangent problem to be
solved at each iteration of a Newton-Raphson algorithm. In case of strongly
nonlinear and heterogeneous problems, this procedure may lead to severe
difficulties. The paper focuses on methods to circumvent these problems, which
can now be expressed using a relatively general framework, even though the
different ingredients of the strategy have emerged separately. We rely here on
the micro-macro framework proposed in (Ladev\`eze, Loiseau, and Dureisseix,
2001). The method proposed in this paper introduces three additional features:
(i) the adaptation of the macro-basis to situations where classical
homogenization does not provide a good preconditioner, (ii) the use of
non-linear relocalization to decrease the number of global problems to be
solved in the case of unevenly distributed non-linearities, (iii) the
adaptation of the approximation of the local Schur complement which governs the
convergence of the proposed iterative technique. Computations of delamination
and delamination-buckling interaction with contact on potentially large
delaminated areas are used to illustrate those aspects
Strict bounding of quantities of interest in computations based on domain decomposition
This paper deals with bounding the error on the estimation of quantities of
interest obtained by finite element and domain decomposition methods. The
proposed bounds are written in order to separate the two errors involved in the
resolution of reference and adjoint problems : on the one hand the
discretization error due to the finite element method and on the other hand the
algebraic error due to the use of the iterative solver. Beside practical
considerations on the parallel computation of the bounds, it is shown that the
interface conformity can be slightly relaxed so that local enrichment or
refinement are possible in the subdomains bearing singularities or quantities
of interest which simplifies the improvement of the estimation. Academic
assessments are given on 2D static linear mechanic problems.Comment: Computer Methods in Applied Mechanics and Engineering, Elsevier,
2015, online previe
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