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 422 articles , 1 standard article )

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  1. Bartels, Sören; Meyer, Frank; Palus, Christian: Simulating self-avoiding isometric plate bending (2022)
  2. Bastian, Peter; Scheichl, Robert; Seelinger, Linus; Strehlow, Arne: Multilevel spectral domain decomposition (2022)
  3. Benavides, Gonzalo A.; Caucao, Sergio; Gatica, Gabriel N.; Hopper, Alejandro A.: A new non-augmented and momentum-conserving fully-mixed finite element method for a coupled flow-transport problem (2022)
  4. Bonaldi, Francesco; Droniou, Jérôme; Masson, Roland; Pasteau, Antoine: Energy-stable discretization of two-phase flows in deformable porous media with frictional contact at matrix-fracture interfaces (2022)
  5. Caucao, Sergio; Oyarzúa, Ricardo; Villa-Fuentes, Segundo; Yotov, Ivan: A three-field Banach spaces-based mixed formulation for the unsteady Brinkman-Forchheimer equations (2022)
  6. Cui, Tao; Wang, Ziming; Xiang, Xueshuang: An efficient neural network method with plane wave activation functions for solving Helmholtz equation (2022)
  7. Faugaret, Antoine; Duguet, Yohann; Fraigneau, Yann; Martin Witkowski, Laurent: A simple model for arbitrary pollution effects on rotating free-surface flows (2022)
  8. Gaudeul, Benoît; Fuhrmann, Jürgen: Entropy and convergence analysis for two finite volume schemes for a Nernst-Planck-Poisson system with ion volume constraints (2022)
  9. Gläser, Dennis; Schneider, Martin; Flemisch, Bernd; Helmig, Rainer: Comparison of cell- and vertex-centered finite-volume schemes for flow in fractured porous media (2022)
  10. Li, Lei; Zhang, Jiaqi; Xu, Zelai; Young, Y.-N.; Feng, James J.; Yue, Pengtao: An arbitrary Lagrangian-Eulerian method for simulating interfacial dynamics between a hydrogel and a fluid (2022)
  11. Li, Tongtong; Yotov, Ivan: A mixed elasticity formulation for fluid-poroelastic structure interaction (2022)
  12. MacLachlan, Scott P.; Madden, Niall; Nhan, Thái Anh: A boundary-layer preconditioner for singularly perturbed convection diffusion (2022)
  13. Oyarzúa, Ricardo; Solano, Manuel; Zúñiga, Paulo: Analysis of an unfitted mixed finite element method for a class of quasi-Newtonian Stokes flow (2022)
  14. Preuss, Adam; Lipoth, Jessica; Spiteri, Raymond J.: When and how to split? A comparison of two IMEX splitting techniques for solving advection-diffusion-reaction equations (2022)
  15. Pulch, Roland: Image analysis for patterns in solutions of reaction-diffusion equations (2022)
  16. Zulfiqar, Umair; Sreeram, Victor; Ahmad, Mian Ilyas; Du, Xin: Frequency-weighted (\mathcalH_2)-optimal model order reduction via oblique projection (2022)
  17. Achdou, Yves; Laurière, Mathieu; Lions, Pierre-Louis: Optimal control of conditioned processes with feedback controls (2021)
  18. Antonietti, Paola F.; De Ponti, Jacopo; Formaggia, Luca; Scotti, Anna: Preconditioning techniques for the numerical solution of flow in fractured porous media (2021)
  19. 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 \textttdeal.II library, Version 9.3 (2021)
  20. Barrett, John W.; Garcke, Harald; Nürnberg, Robert: Stable approximations for axisymmetric Willmore flow for closed and open surfaces (2021)

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