Sparse supernodal solver using block low-rank compression: Design, performance and analysis

G Pichon, E Darve, M Faverge, P Ramet… - Journal of computational …, 2018 - Elsevier
This paper presents two approaches using a Block Low-Rank (BLR) compression technique
to reduce the memory footprint and/or the time-to-solution of the sparse supernodal solver …

An algebraic sparsified nested dissection algorithm using low-rank approximations

L Cambier, C Chen, EG Boman, S Rajamanickam… - SIAM Journal on Matrix …, 2020 - SIAM
We propose a new algorithm for the fast solution of large, sparse, symmetric positive-definite
linear systems, spaND (sparsified Nested Dissection). It is based on nested dissection …

Hierarchical orthogonal factorization: Sparse least squares problems

A Gnanasekaran, E Darve - Journal of Scientific Computing, 2022 - Springer
In this work, we develop a fast hierarchical solver for solving large, sparse least squares
problems. We build upon the algorithm, spaQR (sparsified QR Gnanasekaran and Darve in …

A robust hierarchical solver for ill-conditioned systems with applications to ice sheet modeling

C Chen, L Cambier, EG Boman… - Journal of …, 2019 - Elsevier
A hierarchical solver is proposed for solving sparse ill-conditioned linear systems in parallel.
The solver is based on a modification of the LoRaSp method, but employs a deferred …

Recursively preconditioned hierarchical interpolative factorization for elliptic partial differential equations

J Feliu-Fabà, KL Ho, L Ying - arxiv preprint arxiv:1808.01364, 2018 - arxiv.org
The hierarchical interpolative factorization for elliptic partial differential equations is a fast
algorithm for approximate sparse matrix inversion in linear or quasilinear time. Its accuracy …

Sparse supernodal solver using block low-rank compression

G Pichon, E Darve, M Faverge… - 2017 IEEE …, 2017 - ieeexplore.ieee.org
This paper presents two approaches using a Block Low-Rank (BLR) compression technique
to reduce the memory footprint and/or the time-to-solution of the sparse supernodal solver …

Hierarchical orthogonal factorization: Sparse square matrices

A Gnanasekaran, E Darve - SIAM Journal on Matrix Analysis and Applications, 2022 - SIAM
In this work, we develop a new fast algorithm, spaQR---sparsified QR---for solving large,
sparse linear systems. The key to our approach lies in using low-rank approximations to …

Sparse hierarchical preconditioners using piecewise smooth approximations of eigenvectors

B Klockiewicz, E Darve - SIAM Journal on Scientific Computing, 2020 - SIAM
When solving linear systems arising from PDE discretizations, iterative methods (such as
conjugate gradient (CG), GMRES, or MINRES) are often the only practical choice. To …

Second‐order accurate hierarchical approximate factorizations for solving sparse linear systems

B Klockiewicz, L Cambier, R Humble… - International Journal …, 2022 - Wiley Online Library
We describe a second‐order accurate approach to sparsifying the off‐diagonal matrix blocks
in the hierarchical approximate factorization methods for solving sparse linear systems …

On the use of low-rank arithmetic to reduce the complexity of parallel sparse linear solvers based on direct factorization techniques

G Pichon - 2018 - inria.hal.science
Solving sparse linear systems is a problem that arises in many scientific applications, and
sparse direct solvers are a time consuming and key kernel for those applications and for …