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 245 articles , 1 standard article )

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  1. Botchev, M. A.; Hanse, A. M.; Uppu, R.: Exponential Krylov time integration for modeling multi-frequency optical response with monochromatic sources (2018)
  2. Camaño, Jessika; Muñoz, Cristian; Oyarzúa, Ricardo: Numerical analysis of a dual-mixed problem in non-standard Banach spaces (2018)
  3. Garcke, Harald; Lam, Kei Fong; Nürnberg, Robert; Sitka, Emanuel: A multiphase Cahn-Hilliard-Darcy model for tumour growth with necrosis (2018)
  4. Kim, Youngdae; Huber, Olivier; Ferris, Michael C.: A structure-preserving pivotal method for affine variational inequalities (2018)
  5. Nicholson, Bethany L.; Wan, Wei; Kameswaran, Shivakumar; Biegler, Lorenz T.: Parallel cyclic reduction strategies for linear systems that arise in dynamic optimization problems (2018)
  6. Sushnikova, Daria A.; Oseledets, Ivan V.: “Compress and eliminate” solver for symmetric positive definite sparse matrices (2018)
  7. Zepeda-Núñez, Leonardo; Demanet, Laurent: Nested domain decomposition with polarized traces for the 2D Helmholtz equation (2018)
  8. Arndt, Daniel; Bangerth, Wolfgang; Davydov, Denis; Heister, Timo; Heltai, Luca; Kronbichler, Martin; Maier, Matthias; Pelteret, Jean-Paul; Turcksin, Bruno; Wells, David: The deal.II library, version 8.5 (2017)
  9. Baňas, L’ubomír; Nürnberg, Robert: Numerical approximation of a non-smooth phase-field model for multicomponent incompressible flow (2017)
  10. Bispen, Georgij; Lukáčová-Medvid’ová, Mária; Yelash, Leonid: Asymptotic preserving IMEX finite volume schemes for low Mach number Euler equations with gravitation (2017)
  11. Boedec, Gwenn; Leonetti, Marc; Jaeger, Marc: Isogeometric FEM-BEM simulations of drop, capsule and vesicle dynamics in Stokes flow (2017)
  12. Camaño, Jessika; Oyarzúa, Ricardo; Tierra, Giordano: Analysis of an augmented mixed-FEM for the Navier-Stokes problem (2017)
  13. Caucao, Sergio; Gatica, Gabriel N.; Oyarzúa, Ricardo; Šebestová, Ivana: A fully-mixed finite element method for the Navier-Stokes/Darcy coupled problem with nonlinear viscosity (2017)
  14. Colmenares, Eligio; Gatica, Gabriel N.; Oyarzúa, Ricardo: An augmented fully-mixed finite element method for the stationary Boussinesq problem (2017)
  15. Discacciati, Marco; Oyarzúa, Ricardo: A conforming mixed finite element method for the Navier-Stokes/Darcy coupled problem (2017)
  16. Faugeras, Blaise; Heumann, Holger: FEM-BEM coupling methods for tokamak plasma axisymmetric free-boundary equilibrium computations in unbounded domains (2017)
  17. Filippone, Salvatore; Cardellini, Valeria; Barbieri, Davide; Fanfarillo, Alessandro: Sparse matrix-vector multiplication on GPGPUs (2017)
  18. Ganesan, Sashikumaar; Lingeshwaran, Shangerganesh: Galerkin finite element method for cancer invasion mathematical model (2017)
  19. Güttel, Stefan; Tisseur, Françoise: The nonlinear eigenvalue problem (2017)
  20. Hintermüller, Michael; Hinze, Michael; Kahle, Christian; Keil, Tobias: Fully adaptive and integrated numerical methods for the simulation and control of variable density multiphase flows governed by diffuse interface models (2017)

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