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:

References in zbMATH (referenced in 393 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. Arndt, Daniel; Bangerth, Wolfgang; Blais, Bruno; Fehling, Marc; Gassmöller, Rene; Heister, Timo; Heltai, Luca; Köcher, Uwe; Kronbichler, Martin; Maier, Matthias; Munch, Peter; Pelteret, Jean-Paul; Proell, Sebastian; Simon, Konrad; Turcksin, Bruno; Wells, David; Zhang, Jiaqi: The deal. II library, version 9.3 (2021)
  4. Barrett, John W.; Garcke, Harald; Nürnberg, Robert: Stable approximations for axisymmetric Willmore flow for closed and open surfaces (2021)
  5. 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)
  6. Bollhöfer, Matthias; Schenk, Olaf; Verbosio, Fabio: A high performance level-block approximate LU factorization preconditioner algorithm (2021)
  7. Colmenares, Eligio; Gatica, Gabriel N.; Miranda, Willian: Analysis of an augmented fully-mixed finite element method for a bioconvective flows model (2021)
  8. 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)
  9. Dastour, Hatef; Liao, Wenyuan: An optimal 13-point finite difference scheme for a 2D Helmholtz equation with a perfectly matched layer boundary condition (2021)
  10. Dedner, Andreas; Giesselmann, Jan; Pryer, Tristan; Ryan, Jennifer K.: Residual estimates for post-processors in elliptic problems (2021)
  11. Endtmayer, Bernhard; Langer, Ulrich; Wick, Thomas: Reliability and efficiency of DWR-type a posteriori error estimates with smart sensitivity weight recovering (2021)
  12. Feng, Xiaobing; Qiu, Hailong: Analysis of fully discrete mixed finite element methods for time-dependent stochastic Stokes equations with multiplicative noise (2021)
  13. Frerichs, Derk; John, Volker: On reducing spurious oscillations in discontinuous Galerkin (DG) methods for steady-state convection-diffusion equations (2021)
  14. García-Archilla, Bosco; John, Volker; Novo, Julia: On the convergence order of the finite element error in the kinetic energy for high Reynolds number incompressible flows (2021)
  15. Garcke, Harald; Nürnberg, Robert: Numerical approximation of boundary value problems for curvature flow and elastic flow in Riemannian manifolds (2021)
  16. 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)
  17. Jha, Abhinav: A residual based a posteriori error estimators for AFC schemes for convection-diffusion equations (2021)
  18. Jolivet, Pierre; Roman, Jose E.; Zampini, Stefano: KSPHPDDM and PCHPDDM: extending PETSc with advanced Krylov methods and robust multilevel overlapping Schwarz preconditioners (2021)
  19. 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)
  20. Liu, Jie; Möller, Matthias; Schuttelaars, Henk M.: Balancing truncation and round-off errors in FEM: one-dimensional analysis (2021)

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