UMFPACK

An ANSI C code for sparse LU factorization is presented that combines a column pre-ordering strategy with a right-looking unsymmetric-pattern multifrontal numerical factorization. The pre-ordering and symbolic analysis phase computes an upper bound on fill-in, work, and memory usage during the subsequent numerical factorization. User-callable routines are provided for ordering and analyzing a sparse matrix, computing the numerical factorization, solving a system with the LU factors, transposing and permuting a sparse matrix, and converting between sparse matrix representations.\parThe simple user interface shields the user from the details of the complex sparse factorization data structures by returning simple handles to opaque objects. Additional user-callable routines are provided for printing and extracting the contents of these opaque objects. An even simpler way to use the package is through its MATLAB interface. UMFPACK is incorporated as a built-in operator in MATLAB 6.5 as $x= A^{-1} {\bold b}$ when $A$ is sparse and unsymmetric. (Source: http://dl.acm.org/)


References in zbMATH (referenced in 378 articles , 1 standard article )

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  1. Achdou, Yves; Laurière, Mathieu; Lions, Pierre-Louis: Optimal control of conditioned processes with feedback controls (2021)
  2. Antonietti, Paola F.; De Ponti, Jacopo; Formaggia, Luca; Scotti, Anna: Preconditioning techniques for the numerical solution of flow in fractured porous media (2021)
  3. Bastian, Peter; Blatt, Markus; Dedner, Andreas; Dreier, Nils-Arne; Engwer, Christian; Fritze, René; Gräser, Carsten; Grüninger, Christoph; Kempf, Dominic; Klöfkorn, Robert; Ohlberger, Mario; Sander, Oliver: The \textscDuneframework: basic concepts and recent developments (2021)
  4. Bollhöfer, Matthias; Schenk, Olaf; Verbosio, Fabio: A high performance level-block approximate LU factorization preconditioner algorithm (2021)
  5. Colmenares, Eligio; Gatica, Gabriel N.; Miranda, Willian: Analysis of an augmented fully-mixed finite element method for a bioconvective flows model (2021)
  6. Dastour, Hatef; Liao, Wenyuan: An optimal 13-point finite difference scheme for a 2D Helmholtz equation with a perfectly matched layer boundary condition (2021)
  7. Dastour, Hatef; Liao, Wenyuan: A generalized optimal fourth-order finite difference scheme for a 2D Helmholtz equation with the perfectly matched layer boundary condition (2021)
  8. Frerichs, Derk; John, Volker: On reducing spurious oscillations in discontinuous Galerkin (DG) methods for steady-state convection-diffusion equations (2021)
  9. Jayasinghe, Savithru; Darmofal, David L.; Allmaras, Steven R.; Dow, Eric; Galbraith, Marshall C.: Upwinding and artificial viscosity for robust discontinuous Galerkin schemes of two-phase flow in mass conservation form (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. Koch, Timo; Gläser, Dennis; Weishaupt, Kilian; Ackermann, Sina; Beck, Martin; Becker, Beatrix; Burbulla, Samuel; Class, Holger; Coltman, Edward; Emmert, Simon; Fetzer, Thomas; Grüninger, Christoph; Heck, Katharina; Hommel, Johannes; Kurz, Theresa; Lipp, Melanie; Mohammadi, Farid; Scherrer, Samuel; Schneider, Martin; Seitz, Gabriele; Stadler, Leopold; Utz, Martin; Weinhardt, Felix; Flemisch, Bernd: DuMu(^\textx 3) -- an open-source simulator for solving flow and transport problems in porous media with a focus on model coupling (2021)
  12. Liu, Jie; Möller, Matthias; Schuttelaars, Henk M.: Balancing truncation and round-off errors in FEM: one-dimensional analysis (2021)
  13. Manimaran, J.; Shangerganesh, L.; Debbouche, Amar: Finite element error analysis of a time-fractional nonlocal diffusion equation with the Dirichlet energy (2021)
  14. Niu, Chunyan; Rui, Hongxing; Hu, Xiaozhe: A stabilized hybrid mixed finite element method for poroelasticity (2021)
  15. Stark, Sebastian: On a certain class of one step temporal integration methods for standard dissipative continua (2021)
  16. Adler, J. H.; Gaspar, F. J.; Hu, X.; Ohm, P.; Rodrigo, C.; Zikatanov, L. T.: Robust preconditioners for a new stabilized discretization of the poroelastic equations (2020)
  17. Arndt, Daniel; Bangerth, Wolfgang; Blais, Bruno; Clevenger, Thomas C.; Fehling, Marc; Grayver, Alexander V.; Heister, Timo; Heltai, Luca; Kronbichler, Martin; Maier, Matthias; Munch, Peter; Pelteret, Jean-Paul; Rastak, Reza; Tomas, Ignacio; Turcksin, Bruno; Wang, Zhuoran; Wells, David: The deal.II library, version 9.2 (2020)
  18. Benavides, Gonzalo A.; Caucao, Sergio; Gatica, Gabriel N.; Hopper, Alejandro A.: A Banach spaces-based analysis of a new mixed-primal finite element method for a coupled flow-transport problem (2020)
  19. Caucao, Sergio; Discacciati, Marco; Gatica, Gabriel N.; Oyarzúa, Ricardo: A conforming mixed finite element method for the Navier-Stokes/Darcy-Forchheimer coupled problem (2020)
  20. Caucao, Sergio; Gatica, Gabriel N.; Oyarzúa, Ricardo; Sánchez, Nestor: A fully-mixed formulation for the steady double-diffusive convection system based upon Brinkman-Forchheimer equations (2020)

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