On the storage requirement in the out-of-core multifrontal method for sparse factorization
ACM Transactions on Mathematical Software (TOMS)
The multifrontal method and paging in sparse Cholesky factorization
ACM Transactions on Mathematical Software (TOMS)
The role of elimination trees in sparse factorization
SIAM Journal on Matrix Analysis and Applications
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
The Multifrontal Solution of Indefinite Sparse Symmetric Linear
ACM Transactions on Mathematical Software (TOMS)
An Unsymmetrized Multifrontal LU Factorization
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
External memory algorithms for factoring sparse matrices
External memory algorithms for factoring sparse matrices
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)
Algorithm 837: AMD, an approximate minimum degree ordering algorithm
ACM Transactions on Mathematical Software (TOMS)
Constructing memory-minimizing schedules for multifrontal methods
ACM Transactions on Mathematical Software (TOMS)
Hybrid scheduling for the parallel solution of linear systems
Parallel Computing - Parallel matrix algorithms and applications (PMAA'04)
SIAM Journal on Matrix Analysis and Applications
An out-of-core sparse Cholesky solver
ACM Transactions on Mathematical Software (TOMS)
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
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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Sparse direct solvers, and in particular multifrontal methods, are methods of choice to solve the large sparse systems of linear equations arising in certain simulation problems. However, they require a large amount of memory (e.g., in comparison to iterative methods). In this context, out-of-core solvers may be employed: disks are used when the required storage exceeds the available physical memory. In this paper, we show how to process the task dependency graph of multifrontal methods in a way that minimizes the input/output (I/O) requirements. From a theoretical point of view, we show that minimizing the storage requirement can lead to a huge volume of I/O compared to directly minimizing the I/O volume. Then experiments on large real-world problems also show that applying standard algorithms to minimize the storage is not always efficient at reducing the volume of I/O and that significant gains can be obtained with the use of our algorithms to minimize I/O. We finally show that efficient memory management algorithms can be applied to all the variants proposed.