Stochastic subspace correction methods and fault tolerance

TL;DR

This paper analyzes stochastic subspace correction methods for solving PDEs, demonstrating their convergence and exploring their potential to enable fault tolerance in unreliable computing environments.

Contribution

It provides convergence results for stochastic subspace correction schemes and discusses their application for fault tolerance in distributed computing.

Findings

Proves convergence in expectation for stochastic correction methods

Shows potential for fault tolerance in unreliable networks

Uses domain decomposition algorithms for PDE discretizations

Abstract

We present convergence results in expectation for stochastic subspace correction schemes and their accelerated versions to solve symmetric positive-definite variational problems, and discuss their potential for achieving fault tolerance in an unreliable compute network. We employ the standard overlapping domain decomposition algorithm for PDE discretizations to discuss the latter aspect.