Direct methods for sparse matrices
Direct methods for sparse matrices
The role of elimination trees in sparse factorization
SIAM Journal on Matrix Analysis and Applications
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)
A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling
SIAM Journal on Matrix Analysis and Applications
The design and implementation of a new out-of-core sparse cholesky factorization method
ACM Transactions on Mathematical Software (TOMS)
Hybrid scheduling for the parallel solution of linear systems
Parallel Computing - Parallel matrix algorithms and applications (PMAA'04)
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)
A supernodal out-of-core sparse Gaussian-elimination method
PPAM'07 Proceedings of the 7th international conference on Parallel processing and applied mathematics
A preliminary out-of-core extension of a parallel multifrontal solver
Euro-Par'06 Proceedings of the 12th international conference on Parallel Processing
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We study the forward and backward substitution phases of a sparse multifrontal factorization. These phases are often neglected in papers on sparse direct factorization but, in many applications, they can be the bottleneck so it is crucial to implement them efficiently. In this work, we assume that the factors have been written on disk during the factorization phase, and we discuss the design of an efficient solution phase. We will look at the issues involved when we are solving the sparse systems on parallel computers and will consider in particular their solution in a limited memory environment when out-of-core working is required. Two different approaches are presented to read data from the disk, with a discussion on the advantages and the drawbacks of each. We present some experiments on realistic test problems using an out-of-core version of a sparse multifrontal code called MUltifrontal Massively Parallel Solver (MUMPS).