On the resilience of a parallel sparse hybrid solver
Résumé
As the computational power of high performance computing (HPC) systems
continues to increase by using a huge number of CPU cores or
specialized processing units, extreme-scale applications are
increasingly prone to faults. As a consequence, the HPC community has
proposed many contributions to design resilient HPC applications, may
these contributions be system-oriented, theoretical or numerical. In
this study we consider an actual fully-featured parallel sparse hybrid
(direct/iterative) linear solver, \maphys, and we propose numerical
remedies to design a resilient version of the solver. The solver being
hybrid, we focus in this study on the iterative solution step, which
is often the dominant step in practice. We furthermore assume that a
separate mechanism ensures fault detection and that a system layer
provides support for setting back the environment (processes, \ldots)
in a running state. The present manuscript therefore focuses on (and
only on) strategies for recovering lost data \emph{after} the fault
has been detected (a separate concern out of the scope of this study)
and \emph{once} the system is back in a running state (another
separate concern not studied here either). The numerical remedies we
propose are twofold. Whenever possible, we exploit the natural data redundancy
between processes from the solver to perform exact recovery through
clever copies over processes. Otherwise, data that has been lost and
is not available anymore on any process is recovered through a
so-called interpolation-restart mechanism. This mechanism is derived
from~\cite{aggr:13} to carefully take into account the properties of
the target hybrid solver. These numerical remedies have been
implemented in the \maphys parallel solver so that we can assess their
efficiency on a large number of processing units (up to $12,288$ CPU
cores) for solving large-scale real-life problems.
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