SuperLU

SuperLU is a general purpose library for the direct solution of large, sparse, nonsymmetric systems of linear equations on high performance machines. The library is written in C and is callable from either C or Fortran. The library routines will perform an LU decomposition with partial pivoting and triangular system solves through forward and back substitution. The LU factorization routines can handle non-square matrices but the triangular solves are performed only for square matrices. The matrix columns may be preordered (before factorization) either through library or user supplied routines. This preordering for sparsity is completely separate from the factorization. Working precision iterative refinement subroutines are provided for improved backward stability. Routines are also provided to equilibrate the system, estimate the condition number, calculate the relative backward error, and estimate error bounds for the refined solutions.

This software is also referenced in ORMS.


References in zbMATH (referenced in 193 articles , 2 standard articles )

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  1. Liu, Xiao; Xia, Jianlin; de Hoop, Maarten V.; Ou, Xiaofeng: Interconnected hierarchical structures for fast direct elliptic solution (2022)
  2. Yue, Xiaoqiang; Wang, Chunqing; Xu, Xiaowen; Wang, Libo; Shu, Shi: A new relaxed splitting preconditioner for multidimensional multi-group radiation diffusion equations (2022)
  3. Zulfiqar, Umair; Sreeram, Victor; Ahmad, Mian Ilyas; Du, Xin: Frequency-weighted (\mathcalH_2)-optimal model order reduction via oblique projection (2022)
  4. Aguirre-Mesa, Andres M.; Garcia, Manuel J.; Aristizabal, Mauricio; Wagner, David; Ramirez-Tamayo, Daniel; Montoya, Arturo; Millwater, Harry: A block forward substitution method for solving the hypercomplex finite element system of equations (2021)
  5. Bollhöfer, Matthias; Schenk, Olaf; Verbosio, Fabio: A high performance level-block approximate LU factorization preconditioner algorithm (2021)
  6. D’Ambra, Pasqua; Durastante, Fabio; Filippone, Salvatore: AMG preconditioners for linear solvers towards extreme scale (2021)
  7. Farrell, Patrick E.; Mitchell, Lawrence; Scott, L. Ridgway; Wechsung, Florian: A Reynolds-robust preconditioner for the Scott-Vogelius discretization of the stationary incompressible Navier-Stokes equations (2021)
  8. Gaillard, Antoine; Keeler, Jack S.; Le Lay, Grégoire; Lemoult, Grégoire; Thompson, Alice B.; Hazel, Andrew L.; Juel, Anne: The life and fate of a bubble in a geometrically perturbed Hele-Shaw channel (2021)
  9. Jæger, Karoline Horgmo; Hustad, Kristian Gregorius; Cai, Xing; Tveito, Aslak: Operator splitting and finite difference schemes for solving the EMI model (2021)
  10. Jolivet, Pierre; Roman, Jose E.; Zampini, Stefano: KSPHPDDM and PCHPDDM: extending PETSc with advanced Krylov methods and robust multilevel overlapping Schwarz preconditioners (2021)
  11. Ke, Yifen; Ma, Changfeng: Prediction-correction matrix splitting iteration algorithm for a class of large and sparse linear systems (2021)
  12. Rodopoulos, Dimitrios C.; Atluri, Satya N.; Polyzos, Demosthenes: A hybrid FPM/BEM scalar potential formulation for field calculation in nonlinear magnetostatic analysis of superconducting accelerator magnets (2021)
  13. Van Niekerk, J., Bakka, H., Rue, H., Schenk, O. : New Frontiers in Bayesian Modeling Using the INLA Package in R (2021) not zbMATH
  14. Balm, Floris; Krikun, Alexander; Romero-Bermúdez, Aurelio; Schalm, Koenraad; Zaanen, Jan: Isolated zeros destroy Fermi surface in holographic models with a lattice (2020)
  15. Beams, Natalie N.; Gillman, Adrianna; Hewett, Russell J.: A parallel shared-memory implementation of a high-order accurate solution technique for variable coefficient Helmholtz problems (2020)
  16. Bollhöfer, Matthias; Schenk, Olaf; Janalik, Radim; Hamm, Steve; Gullapalli, Kiran: State-of-the-art sparse direct solvers (2020)
  17. Cremon, Matthias A.; Castelletto, Nicola; White, Joshua A.: Multi-stage preconditioners for thermal-compositional-reactive flow in porous media (2020)
  18. Dutra do Carmo, E. G.; Leal, R. M. T.; Mansur, W. J.: A new scheme to obtain pollution-free solution for plane waves and to generate a continuous Petrov-Galerkin method for the Helmholtz problem (2020)
  19. Etling, Tommy; Herzog, Roland; Loayza, Estefanía; Wachsmuth, Gerd: First and second order shape optimization based on restricted mesh deformations (2020)
  20. Glusa, Christian; Boman, Erik G.; Chow, Edmond; Rajamanickam, Sivasankaran; Szyld, Daniel B.: Scalable asynchronous domain decomposition solvers (2020)

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