Resilient asynchronous primal Schur method

This paper introduces the application of asynchronous iterations theory within the framework of the primal Schur domain decomposition method. A suitable relaxation scheme is designed, whose asynchronous convergence is established under classical spectral radius conditions. For the usual case where local Schur complement matrices are not constructed, suitable splittings based only on explicitly generated matrices are provided. Numerical experiments are conducted on a supercomputer for both Poisson’s and linear elasticity problems. The asynchronous Schur solver outperformed the classical conjugate-gradient-based one in case of computing node failures.