On the storage requirement in the out-of-core multifrontal method for sparse factorization
ACM Transactions on Mathematical Software (TOMS)
The input/output complexity of sorting and related problems
Communications of the ACM
The influence of relaxed supernode partitions on the multifrontal method
ACM Transactions on Mathematical Software (TOMS)
The role of elimination trees in sparse factorization
SIAM Journal on Matrix Analysis and Applications
ACM Transactions on Mathematical Software (TOMS)
Block sparse Cholesky algorithms on advanced uniprocessor computers
SIAM Journal on Scientific Computing
A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
SIAM Journal on Scientific Computing
Efficient Methods for Out-of-Core Sparse Cholesky Factorization
SIAM Journal on Scientific Computing
A New Implementation of Sparse Gaussian Elimination
ACM Transactions on Mathematical Software (TOMS)
The Multifrontal Solution of Indefinite Sparse Symmetric Linear
ACM Transactions on Mathematical Software (TOMS)
External memory algorithms for factoring sparse matrices
External memory algorithms for factoring sparse matrices
The design and implementation of a new out-of-core sparse cholesky factorization method
ACM Transactions on Mathematical Software (TOMS)
Optimal sparse matrix dense vector multiplication in the I/O-model
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
Algorithm 891: A Fortran virtual memory system
ACM Transactions on Mathematical Software (TOMS)
An out-of-core sparse Cholesky solver
ACM Transactions on Mathematical Software (TOMS)
Proceedings of the twenty-second annual ACM symposium on Parallelism in algorithms and architectures
Reducing the I/O Volume in Sparse Out-of-core Multifrontal Methods
SIAM Journal on Scientific Computing
The university of Florida sparse matrix collection
ACM Transactions on Mathematical Software (TOMS)
Communication-optimal Parallel and Sequential Cholesky Decomposition
SIAM Journal on Scientific Computing
A preliminary out-of-core extension of a parallel multifrontal solver
Euro-Par'06 Proceedings of the 12th international conference on Parallel Processing
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
SDAFT: a novel scalable data access framework for parallel BLAST
DISCS-2013 Proceedings of the 2013 International Workshop on Data-Intensive Scalable Computing Systems
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Direct methods for solving sparse linear systems are robust and typically exhibit good performance, but often require large amounts of memory due to fill-in. Many industrial applications use out-of-core techniques to mitigate this problem. However, parallelizing sparse out-of-core solvers poses some unique challenges because accessing secondary storage introduces serialization and I/O overhead. We analyze the data-movement costs and memory versus parallelism trade-offs in a shared-memory parallel out-of-core linear solver for sparse symmetric systems. We propose an algorithm that uses a novel memory management scheme and adaptive task parallelism to reduce the data-movement costs. We present experiments to show that our solver is faster than existing out-of-core sparse solvers on a single core, and is more scalable than the only other known shared-memory parallel out-of-core solver. This work is also directly applicable at the node level in a distributed-memory parallel scenario.