A Fault-Tolerant Parallel Algorithm for Iterative Solution of the Laplace Equation

Algorithm based fault tolerance is an inexpensive method of achieving fault tolerance without requiring any hardware modifications. Algorithm-based schemes have been proposed for a wide variety of numerical applications. However, for a particular class of numerical applications, namely those involving the iterative solution of linear systems, there exist almost no fault-tolerant algorithms in the literature. In this paper, we describe a fault-tolerant version of a parallel algorithm for iteratively solving the Laplace equation over a grid.