On the Resilience of Parallel Sparse Hybrid Solvers

Abstract

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. Consequently, the HPC community has proposed many contributions to design resilient HPC applications. These contributions may 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, . . . ) in a running state. The present manuscript therefore focuses on (and only on) strategies for recovering lost data after the fault has been detected (a separate concern beyond the scope of this study), once the system is restored (another separate concern not studied here). 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 no longer available on any process is recovered through a so-called interpolation-restart mechanism. This mechanism is derived from [1] by carefully taking 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.

Stochastic subspace correction methods and fault tolerance

“…where Ω is a (nice) domain in R We consider Schwarz iterative methods (also called subspace correction methods) for solving (1). The underlying space splitting is given by a collection {V i } i=0,1,...,n of n + 1 separable real Hilbert spaces, each equipped with a spectrally equivalent scalar product a i (·, ·) and norm a i (v i , v i ) 1/2 , and bounded linear operators R i :…”

“…In the m-th step of a Schwarz iterative method for solving (1), a certain finite set I m ⊂ {0, 1, . .…”

Resilience and fault tolerance in high-performance computing for numerical weather and climate prediction

“…Interpolation-Restart (IR) techniques are designed to cope with node crashes (hard faults) in a parallel distributed environment (Agullo et al, 2015(Agullo et al, , 2017(Agullo et al, , 2016a(Agullo et al, , 2016b. The methods can be designed at the algebraic level for the solution both of linear systems and of eigenvalue problems.…”

Interpolation-Restart Strategies for Resilient Eigensolvers

“…In this paper, we extend the interpolation-restart (IR) strategies introduced for the solution of linear systems [1,21,3] to a few state-of-the-art eigensolvers. More precisely, the Arnoldi [6], Implicitly restarted Arnoldi [22], subspace iteration [30], and Jacobi-Davidson [35] algorithms are being revisited to make them resilient in the presence of faults.…”