June 22 – Valentine Rey: Goal-oriented error control within non-overlapping domain decomposition methods to solve elliptic problems

Valentine Rey: Thursday 22 June at 3 pm, A415 Inria Paris.
Domain decomposition methods are robust and efficient methods to solve mechanical problems with several million degrees of freedom. Taking advantage of increasing performances of computers, they exploit the clusters-parallel architecture and are numerically scalable. Verification has been widely developed since 1980’s and proposes tools to estimate the distance between the unknown exact solution of continuous problem and the computed solution. Among those techniques, estimators based on error in constitutive relation provide constant-free upper bounds and are available for varied range of problems.
In this talk, we present techniques for steering parallel computation by objective of accuracy on quantities of interest. It relies on a parallel error estimator that provides strict guaranteed upper bound and separates the algebraic error (due to the use of iterative solver) from the discretization error (due to the finite element method). This estimator enables to adapt the solver’s stopping criterion to the discretization, which avoids over resolution and useless iterations. In [*], the estimator is used for goal-oriented error estimation and classical bounds for quantities of interest are rewritten in order to separate sources of error. Finally, we benefit the information provided by the error estimator and the Krylov subspaces built during the resolution to set an auto-adaptive strategy (adaptive remeshing and recycling search directions).

*V. Rey, P. Gosselet, C. Rey, Strict bounding of quantities of interest in computations based on domain decomposition, Computer Methods in Applied Mechanics and Engineering. 2015 Apr 15;287:212-28

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