The computation and communication complexity of a parallel banded system solver
ACM Transactions on Mathematical Software (TOMS)
SIAM Journal on Scientific and Statistical Computing
A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
SIAM Journal on Scientific Computing
The Design and Use of Algorithms for Permuting Large Entries to the Diagonal of Sparse Matrices
SIAM Journal on Matrix Analysis and Applications
Practical Parallel Band Triangular System Solvers
ACM Transactions on Mathematical Software (TOMS)
Algorithm 575: Permutations for a Zero-Free Diagonal [F1]
ACM Transactions on Mathematical Software (TOMS)
Preconditioning Highly Indefinite and Nonsymmetric Matrices
SIAM Journal on Scientific Computing
A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling
SIAM Journal on Matrix Analysis and Applications
Solving unsymmetric sparse systems of linear equations with PARDISO
Future Generation Computer Systems - Special issue: Selected numerical algorithms
Mathematical Programming: Series A and B
Hybrid scheduling for the parallel solution of linear systems
Parallel Computing - Parallel matrix algorithms and applications (PMAA'04)
A parallel hybrid banded system solver: the SPIKE algorithm
Parallel Computing - Parallel matrix algorithms and applications (PMAA'04)
Analysis of the Truncated SPIKE Algorithm
SIAM Journal on Matrix Analysis and Applications
On some parallel banded system solvers
Parallel Computing
TRACEMIN-Fiedler: a parallel algorithm for computing the Fiedler vector
VECPAR'10 Proceedings of the 9th international conference on High performance computing for computational science
Performance models for the Spike banded linear system solver
Scientific Programming
A domain-decomposing parallel sparse linear system solver
Journal of Computational and Applied Mathematics
A threaded SPIKE algorithm for solving general banded systems
Parallel Computing
The Journal of Supercomputing
An Empirical Analysis of the Performance of Preconditioners for SPD Systems
ACM Transactions on Mathematical Software (TOMS)
Journal of Parallel and Distributed Computing
PARA'12 Proceedings of the 11th international conference on Applied Parallel and Scientific Computing
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The availability of large-scale computing platforms comprised of tens of thousands of multicore processors motivates the need for the next generation of highly scalable sparse linear system solvers. These solvers must optimize parallel performance, processor (serial) performance, as well as memory requirements, while being robust across broad classes of applications and systems. In this paper, we present a new parallel solver that combines the desirable characteristics of direct methods (robustness) and effective iterative solvers (low computational cost), while alleviating their drawbacks (memory requirements, lack of robustness). Our proposed hybrid solver is based on the general sparse solver PARDISO, and the "Spike" family of hybrid solvers. The resulting algorithm, called PSPIKE, is as robust as direct solvers, more reliable than classical preconditioned Krylov subspace methods, and much more scalable than direct sparse solvers. We support our performance and parallel scalability claims using detailed experimental studies and comparison with direct solvers, as well as classical preconditioned Krylov methods.