The design of I/O-efficient sparse direct solvers
Proceedings of the 2001 ACM/IEEE conference on Supercomputing
Impact of reordering on the memory of a multifrontal solver
Parallel Computing - Parallel matrix algorithms and applications (PMAA '02)
The design and implementation of a new out-of-core sparse cholesky factorization method
ACM Transactions on Mathematical Software (TOMS)
Adaptive paging for a multifrontal solver
Proceedings of the 18th annual international conference on Supercomputing
An out-of-core sparse symmetric-indefinite factorization method
ACM Transactions on Mathematical Software (TOMS)
An out-of-core sparse Cholesky solver
ACM Transactions on Mathematical Software (TOMS)
On the I/O Volume in Out-of-Core Multifrontal Methods with a Flexible Allocation Scheme
High Performance Computing for Computational Science - VECPAR 2008
Scaling and pivoting in an out-of-core sparse direct solver
ACM Transactions on Mathematical Software (TOMS)
Analysis of the solution phase of a parallel multifrontal approach
Parallel Computing
Reducing the I/O volume in an out-of-core sparse multifrontal solver
HiPC'07 Proceedings of the 14th international conference on High performance computing
Reducing the I/O Volume in Sparse Out-of-core Multifrontal Methods
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
Managing data-movement for effective shared-memory parallelization of out-of-core sparse solvers
SC '12 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
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We consider the problem of sparse Cholesky factorization with limited main memory. The goal is to efficiently factor matrices whose Cholesky factors essentially fill the available disk storage, using very little memory (as little as 16 Megabytes (MBytes)). This would enable very large industrial problems to be solved with workstations of very modest cost.We consider three candidate algorithms. Each is based on a partitioning of the matrix into panels. The first is a robust, out-of-core multifrontal method that keeps the factor, the stack, and the large frontal matrices on disk. The others are left-looking methods. We find that straightforward implementations of all of them suffer from excessive disk I/O for large problems that arise in interior-point algorithms for linear programming. We introduce several improvements to these simple out-of-core methods and find that a left-looking method that nevertheless uses the multifrontal algorithm for portions of the matrix (subtrees of the supernodal elimination tree whose multifrontal stack fits in memory) is very effective. With 32 Mbytes of main memory, it achieves over 77% of its in-core performance on all but one of our 12 test matrices (67% in that one case), even though the size of the factor is, in all cases, hundreds of millions or even billions of bytes.