Deflation of conjugate gradients with applications to boundary value problems
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
A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
SIAM Journal on Scientific Computing
A Restricted Additive Schwarz Preconditioner for General Sparse Linear Systems
SIAM Journal on Scientific Computing
An updated set of basic linear algebra subprograms (BLAS)
ACM Transactions on Mathematical Software (TOMS)
On the Construction of Deflation-Based Preconditioners
SIAM Journal on Scientific Computing
A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling
SIAM Journal on Matrix Analysis and Applications
PASTIX: a high-performance parallel direct solver for sparse symmetric positive definite systems
Parallel Computing - Parallel matrix algorithms and applications
SIAM Journal on Numerical Analysis
Solving unsymmetric sparse systems of linear equations with PARDISO
Future Generation Computer Systems - Special issue: Selected numerical algorithms
Hybrid scheduling for the parallel solution of linear systems
Parallel Computing - Parallel matrix algorithms and applications (PMAA'04)
deal.II—A general-purpose object-oriented finite element library
ACM Transactions on Mathematical Software (TOMS)
PT-Scotch: A tool for efficient parallel graph ordering
Parallel Computing
Journal of Scientific Computing
Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book
Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book
Parallel geometric-algebraic multigrid on unstructured forests of octrees
SC '12 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
A parallel two-level preconditioner for cosmic microwave background map-making
SC '12 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
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Domain decomposition methods are, alongside multigrid methods, one of the dominant paradigms in contemporary large-scale partial differential equation simulation. In this paper, a lightweight implementation of a theoretically and numerically scalable preconditioner is presented in the context of overlapping methods. The performance of this work is assessed by numerical simulations executed on thousands of cores, for solving various highly heterogeneous elliptic problems in both 2D and 3D with billions of degrees of freedom. Such problems arise in computational science and engineering, in solid and fluid mechanics. While focusing on overlapping domain decomposition methods might seem too restrictive, it will be shown how this work can be applied to a variety of other methods, such as non-overlapping methods and abstract deflation based preconditioners. It is also presented how multilevel preconditioners can be used to avoid communication during an iterative process such as a Krylov method.