The construction of preconditioners for elliptic problems by substructuring. I
Mathematics of Computation
Iterative methods for the solution of elliptic problems on regions partitioned into substructures
SIAM Journal on Numerical Analysis
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
ScaLAPACK user's guide
The Multifrontal Solution of Indefinite Sparse Symmetric Linear
ACM Transactions on Mathematical Software (TOMS)
A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling
SIAM Journal on Matrix Analysis and Applications
ACM Transactions on Mathematical Software (TOMS)
Modified Gram-Schmidt (MGS), Least Squares, and Backward Stability of MGS-GMRES
SIAM Journal on Matrix Analysis and Applications
Parallel scalability study of hybrid preconditioners in three dimensions
Parallel Computing
Hierarchical Krylov and nested Krylov methods for extreme-scale computing
Parallel Computing
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Large-scale scientific simulations are nowadays fully integrated in many scientific and industrial applications. Many of these simulations rely on modelisations based on PDEs that lead to the solution of huge linear or nonlinear systems of equations involving millions of unknowns. In that context, the use of large high performance computers in conjunction with advanced fully parallel and scalable numerical techniques is mandatory to efficiently tackle these problems. In this paper, we consider a parallel linear solver based on a domain decomposition approach. Its implementation naturally exploits two levels of parallelism, that offers the flexibility to combine the numerical and the parallel implementation scalabilities. The combination of the two levels of parallelism enables an optimal usage of the computing resource while preserving attractive numerical performance. Consequently, such a numerical technique appears as a promising candidate for intensive simulations on massively parallel platforms. The robustness and parallel numerical performance of the solver is investigated on large challenging linear systems arising from the finite element discretization in structural mechanics applications.