1. Coarse-grid preconditioner

To set out the various methods in a simple framework, we have considered decompositions into two sub-domains in the previous sections. In reality, parallel computers have thousands or even hundreds of thousands of processors, and domains need to be decomposed into as many sub-domains as possible to ensure that the resolution process is properly parallelized. But all the iterative methods we've seen lose their efficiency as the number of sub-domains increases. These methods are said to be unscalable. We need to add a new component to all these methods to obtain scalable methods, and this is the subject of this section.