22,074 research outputs found
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
Construction and Application of an AMR Algorithm for Distributed Memory Computers
While the parallelization of blockstructured adaptive mesh refinement techniques is relatively straight-forward on shared memory architectures, appropriate distribution strategies for the emerging generation of distributed
memory machines are a topic of on-going research. In this paper, a locality-preserving domain decomposition is proposed that partitions the entire AMR hierarchy from the base level on. It is shown that the approach reduces the
communication costs and simplifies the implementation. Emphasis is put on the effective parallelization of the flux correction procedure at coarse-fine boundaries, which is indispensable for conservative finite volume schemes. An
easily reproducible standard benchmark and a highly resolved parallel AMR
simulation of a diffracting hydrogen-oxygen detonation demonstrate the proposed
strategy in practice
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