Fault tolerant numerical solvers

Soft errors are increasing in modern computer systems. These faults can corrupt the results of numerical solvers commonly used in scientific and electromagnetic simulations. If the severity of a bitflip is high, then our numerical code might never converge. There are several techniques to address the issue of soft faults in numerical solvers. Self-stabilizing and Algorithm-Based Fault Tolerance (ABFT) techniques are notably the most popular choice when it comes to designing a fault tolerant scheme. Selfstabilizing numerical methods have been developed to retrieve numerical stability in the presence of faults at the cost of running computation-intensive reliable iterations. Our work presents efficient techniques to determine when to execute the correction loop in Self-stabilizing conjugate gradient methods (SS-CG). The proposed adaptive-F and invariant check strategies have low overheads compared to current techniques used in self-stabilizing methods. Developing resiliency in the presence of multiple faults is another challenging aspect of fault tolerance. Most researchers consider the effect of a single bitflip while designing their fault tolerant schemes. In this thesis, we address the importance of addressing multiple faults and propose a novel recursive block checkSum strategy to localize errors and correct them in sparse numerical code.M.S.Includes bibliographical referencesby Aaditya Shukl