A column pre-ordering strategy for the unsymmetric-pattern multifrontal method

By Timothy A. Davis. TOMS, 2004

447 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/9892b0757d86b9ea1960260b818a06c21e63fdeb

How researchers see this paper

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In Computational Theory and Mathematics

1. Oliver Rheinbach
2. Axel Klawonn
3. Z. Qian
4. Weng Cho Chew
5. Denis Sipp
6. Yifan Hu
7. G. Hou
8. Vijay Vittal

In Numerical Analysis

1. Z. Qian
2. Weng Cho Chew
3. Denis Sipp
4. Oliver Rheinbach
5. Axel Klawonn
6. G. Hou
7. Thomas Zwinger
8. A. Lebedev

Citations in the corpus

• Sensitivity analysis and passive control of cylinder flow (2008, methodology): “These matrices are sparse and their inverses are handled using the UMFPACK library, which consists of a sparse direct LU solver (see Davis & Duff 1997; Davis 2004).”
• Inexact FETI‐DP methods (2007, methodology): “We use renumbering [40] before we carry out the incomplete factorization.”
• Global stability of base and mean flows: a general approach and its applications to cylinder and open cavity flows (2007, methodology): “Note that all matrices are built thanks to the FreeFEM++ software (see www.freefem.org), while all matrix inverses are handled using the UMFPACK library, which uses a sparse direct LU solver based on an unsymmetric-pattern multifrontal method (see Davis & Duff 1997; Davis 2004).”
• Generalized Impedance Boundary Condition for Conductor Modeling in Surface Integral Equation (2007, methodology): “The multifrontal method [18] is adopted for the inversion of the sparse matrices .”
• The university of Florida sparse matrix collection (2011, methodology): “…web connectivity matrices [Kamvar 2008; Kamvar et al. 2004; Page et al. 1998], which have existed only since the mid 1990’s. Sparse matrix algorithm developers use the matrices in the Collection to develop their methods, since theoretical asymptotic time/memory complexity analysis only goes so far.”
• A smoothed particle hydrodynamics model for reactive transport and mineral precipitation in porous and fractured porous media (2007, methodology): “The solver uses the linear solver UMFPACK [Davis, 2004] for matrix inversion and a damped Newton method [Deuflehard, 1974] for nonlinear iteration.”
• Trajectory Sensitivity Based Preventive Control of Voltage Instability Considering Load Uncertainties (2012, methodology): “UMFPACK is one of the fastest packages for solving unsymmetric sparse linear systems using the unsymmetric multifrontal method [24]–[27].”
• Discontinuous Galerkin methods in nanophotonics (2011, methodology): “To this end, sophisticated column-reordering strategies are employed [80, 81].”
• The ISMIP-HOM benchmark experiments performed using the Finite-Element code Elmer (2008, methodology): “4 Specific characteristics of experiments The aim of this part is to present some specific results obtained for each of the experiments. A complete description of all the ISMIP-HOM experiments can be found in Pattyn and Payne (2006) (http://homepages.ulb.ac.be/∼fpattyn/ismip/) and in Pattyn et al. (”
• Fast Full-Wave Surface Integral Equation Solver for Multiscale Structure Modeling (2009, methodology): “A fast direct solver, such as the multifrontal method [33], can be used to factorize it and store it for back-substitution.”