Asynchronous multisplitting-based primal Schur method

This paper presents a new scalable asynchronous domain decomposition method which significantly outperforms the recent two-level asynchronous restricted additive Schwarz (RAS) method. The novel approach consists of considering the classical primal Schur complement framework and solving the interface problem using a multisplitting relaxation based on a weighted additive Schwarz preconditioner. The computational model does not require any significant implementation effort compared to an asynchronous RAS solver. Experiments were conducted on a linear elasticity test case, and the results clearly show the practical superiority of the new asynchronous method, which is even competitive with its conjugate gradient counterpart. •Coupling multisplitting and substructuring approaches.•Applying Schwarz-type decomposition to Schur-complement-based interface problem.•Asynchronous implementation pattern with multiplicative interface coarse-space correction.•Practical superiority over the two-level restricted additive Schwarz method.•Practical competitiveness with the two-level conjugate-gradient-based primal Schur method.