Partially Updated Restricted Additive Schwarz Preconditioner

摘要

The utilization of domain decomposition preconditioners allows us to update only certain parts of the preconditioner, keeping the other ones constant. In the context of parallel computing, this partial update can be computed asynchronously, that is to say that the time-stepper computations are not stopped if the update is not available. Finally, numerical results showed that superlinear speedups can be obtained by adding processes dedicated to the LU factorizations. Furthermore, the preconditioner is continually updated which makes the results less sensitive to the frequency of global update. In this paper, all subdomain parts of the preconditioner are successively updated, but it would be relevant to update more often the LU factorizations associated to subdomains with high local nonlinearities. Then, the AsRAS preconditioner should benefit from a numerical criterion that helps to choose which subdomains need the more an update.