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 212 articles , 1 standard article )

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  1. 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)
  2. Baňas, L’ubomír; Nürnberg, Robert: Numerical approximation of a non-smooth phase-field model for multicomponent incompressible flow (2017)
  3. Camaño, Jessika; Oyarzúa, Ricardo; Tierra, Giordano: Analysis of an augmented mixed-FEM for the Navier-Stokes problem (2017)
  4. 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)
  5. Colmenares, Eligio; Gatica, Gabriel N.; Oyarzúa, Ricardo: An augmented fully-mixed finite element method for the stationary Boussinesq problem (2017)
  6. Discacciati, Marco; Oyarzúa, Ricardo: A conforming mixed finite element method for the Navier-Stokes/Darcy coupled problem (2017)
  7. Ganesan, Sashikumaar; Lingeshwaran, Shangerganesh: Galerkin finite element method for cancer invasion mathematical model (2017)
  8. Kuo, Frances Y.; Scheichl, Robert; Schwab, Christoph; Sloan, Ian H.; Ullmann, Elisabeth: Multilevel quasi-Monte Carlo methods for lognormal diffusion problems (2017)
  9. Oyarzúa, Ricardo; Zúñiga, Paulo: Analysis of a conforming finite element method for the Boussinesq problem with temperature-dependent parameters (2017)
  10. Reisinger, Christoph; Rotaetxe Arto, Julen: Boundary treatment and multigrid preconditioning for semi-Lagrangian schemes applied to Hamilton-Jacobi-Bellman equations (2017)
  11. Robert C. Kirby, Lawrence Mitchell: Solver composition across the PDE/linear algebra barrier (2017) arXiv
  12. Suñagua, Porfirio; Oliveira, Aurelio R.L.: A new approach for finding a basis for the splitting preconditioner for linear systems from interior point methods (2017)
  13. Zhu, Yao; Sameh, Ahmed H.: $\textPSPIKE+$: A family of parallel hybrid sparse linear system solvers (2017)
  14. Adler, J.H.; Emerson, D.B.; MacLachlan, S.P.; Manteuffel, T.A.: Constrained optimization for liquid crystal equilibria (2016)
  15. Bangerth, Wolfgang; Davydov, Denis; Heister, Timo; Heltai, Luca; Kanschat, Guido; Kronbichler, Martin; Maier, Matthias; Turcksin, Bruno; Wells, David: The deal.II library, version 8.4 (2016)
  16. Barrett, John W.; Garcke, Harald; Nürnberg, Robert: Computational parametric Willmore flow with spontaneous curvature and area difference elasticity effects (2016)
  17. Benninghoff, Heike; Garcke, Harald: Segmentation and restoration of images on surfaces by parametric active contours with topology changes (2016)
  18. Botchev, Mikhail A.: Krylov subspace exponential time domain solution of Maxwell’s equations in photonic crystal modeling (2016)
  19. Bouillaguet, Charles; Delaplace, Claire: Sparse Gaussian elimination modulo $p$: an update (2016)
  20. Carraro, Thomas; Friedmann, Elfriede; Gerecht, Daniel: Coupling vs decoupling approaches for PDE/ODE systems modeling intercellular signaling (2016)

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