2,898 research outputs found
Substructured formulations of nonlinear structure problems - influence of the interface condition
We investigate the use of non-overlapping domain decomposition (DD) methods
for nonlinear structure problems. The classic techniques would combine a global
Newton solver with a linear DD solver for the tangent systems. We propose a
framework where we can swap Newton and DD, so that we solve independent
nonlinear problems for each substructure and linear condensed interface
problems. The objective is to decrease the number of communications between
subdomains and to improve parallelism. Depending on the interface condition, we
derive several formulations which are not equivalent, contrarily to the linear
case. Primal, dual and mixed variants are described and assessed on a simple
plasticity problem.Comment: in International Journal for Numerical Methods in Engineering, Wiley,
201
Objective multiscale analysis of random heterogeneous materials
The multiscale framework presented in [1, 2] is assessed in this contribution for a study of random heterogeneous materials. Results are compared to direct numerical simulations (DNS) and the sensitivity to user-defined parameters such as the domain decomposition type and initial coarse scale resolution is reported. The parallel performance of the implementation is studied for different domain decompositions
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
A scalable parallel finite element framework for growing geometries. Application to metal additive manufacturing
This work introduces an innovative parallel, fully-distributed finite element
framework for growing geometries and its application to metal additive
manufacturing. It is well-known that virtual part design and qualification in
additive manufacturing requires highly-accurate multiscale and multiphysics
analyses. Only high performance computing tools are able to handle such
complexity in time frames compatible with time-to-market. However, efficiency,
without loss of accuracy, has rarely held the centre stage in the numerical
community. Here, in contrast, the framework is designed to adequately exploit
the resources of high-end distributed-memory machines. It is grounded on three
building blocks: (1) Hierarchical adaptive mesh refinement with octree-based
meshes; (2) a parallel strategy to model the growth of the geometry; (3)
state-of-the-art parallel iterative linear solvers. Computational experiments
consider the heat transfer analysis at the part scale of the printing process
by powder-bed technologies. After verification against a 3D benchmark, a
strong-scaling analysis assesses performance and identifies major sources of
parallel overhead. A third numerical example examines the efficiency and
robustness of (2) in a curved 3D shape. Unprecedented parallelism and
scalability were achieved in this work. Hence, this framework contributes to
take on higher complexity and/or accuracy, not only of part-scale simulations
of metal or polymer additive manufacturing, but also in welding, sedimentation,
atherosclerosis, or any other physical problem where the physical domain of
interest grows in time
Shift-invert diagonalization of large many-body localizing spin chains
We provide a pedagogical review on the calculation of highly excited
eigenstates of disordered interacting quantum systems which can undergo a
many-body localization (MBL) transition, using shift-invert exact
diagonalization. We also provide an example code at
https://bitbucket.org/dluitz/sinvert_mbl/. Through a detailed analysis of the
simulational parameters of the random field Heisenberg spin chain, we provide a
practical guide on how to perform efficient computations. We present data for
mid-spectrum eigenstates of spin chains of sizes up to . This work is
also geared towards readers with interest in efficiency of parallel sparse
linear algebra techniques that will find a challenging application in the MBL
problem
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