This Innovation Study uses an asynchronous linear solver technology, focusing on a new approach for parallel computing. Unlike traditional methods that rely on global sums and synchronized pairwise communication, this study operates without these constraints. Asynchronous techniques offer advantages by eliminating synchronization barriers, thereby enhancing the efficiency of computer systems through reduced periods of inactivity. Furthermore, their inherent ability to tolerate communication latencies enhances fault tolerance, ensuring robustness in complex computing environments. In addition, asynchronous methods unlock the potential for leveraging power-saving and energy-efficient features offered by modern hardware architectures. This positions them as promising solutions for highly parallel and diverse hardware platforms.

The experimental concept is based on the classic conjugate gradient (CG) method, adapted for partitioned data environments. This study however diverges significantly from conventional usage by treating each partition as an independent problem. Consequently, it advances a Krylov subspace for each partition autonomously, without requiring global synchronization. Global problem coupling and convergence are achieved by perturbing the local solution using information from remote partitions. Crucially, these perturbations are updated asynchronously, eliminating the need for complete partition progress synchronization. Through empirical validation and performance analysis, this study demonstrates the efficacy and potential of the asynchronous linear solver concept. By embracing the principles of asynchrony and partitioned computation, this technology is able to revolutionize scalable and fault-tolerant parallel computing paradigms, as well as enhance computational efficiency.