Accelerated Restricted Additive Schwarz method for asynchronous processing

This paper examines the parallel efficiency of both synchronous and asynchronous domain decomposition methods (DDMs), when solving algebraic systems derived from the discretization of partial differential equations (PDEs). We consider two separate approaches. First, we use the Restricted Additive Schwarz (RAS) domain decomposition solver as our primary DDM. Second, we integrate an acceleration method to minimize computational costs. For both approaches, we assess the parallel efficiency through various numerical experiments. Our results indicate that the asynchronous method provides a significant improvement in computational speed compared to the synchronous method, especially in large-scale problems. Additionally, the integration of the acceleration method further enhances the performance, reducing the overall computational time.