Algorithm 832: UMFPACK V4.3---an unsymmetric-pattern multifrontal method

By Timothy A. Davis. TOMS, 2004

1,648 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Electrical and Electronic Engineering, Hardware and Architecture

View Paper: https://www.semanticscholar.org/paper/6f7a71576faaca16f5f9716dfe107c84d1ee5bb6

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Citations in the corpus

THE r-PROCESS NUCLEOSYNTHESIS IN THE VARIOUS JET-LIKE EXPLOSIONS OF MAGNETOROTATIONAL CORE-COLLAPSE SUPERNOVAE (2015, methodology): “At each time step the network code solves linear equation systems of all isotopes based on Equation (8) by matrix inversion, using a sparse matrix solver, UMFPACK 2 (Davis 2004).”
Efficient augmented Lagrangian‐type preconditioning for the Oseen problem using Grad‐Div stabilization (2013, methodology): “The inner blocks are solved using the direct solver UMFPACK, see [36].”
Level set topology optimization of structural problems with interface cohesion (2017, methodology): “The linearized sub-problems within the Newton iterations and the adjoint sensitivity analysis are solved using the UMFPACK direct solver [76] for the 2D examples and a generalized minimal residual iterative solver with incomplete LU factorization [77] for the 3D examples.”
Circuit quantum electrodynamics (2010, methodology): “The matrix M is very sparse, unsymmetric, and not so large that iterative methods are needed, consequently a good choice was the multifrontal method as implemented in Mathematica based on UMFPACK [73], for generating an LU decomposition of M.”
Optimal Step Nonrigid ICP Algorithms for Surface Registration (2007, methodology): “The system of linear equations that arises in each step of the N-ICP-A and N-ICP-T methods was solved using the UMFPACK library [6].”
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.”
Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control (2018, methodology): “In our implementation the solvers for the linear systems involved are the sparse direct solvers from the UMFPACK library (Davis, 2004).”
divand-1.0: n -dimensional variational data analysis for ocean observations (2013, methodology): “The solver based on SuiteSparse (Davis, 2004a,b) can be used directly if the matrix R \ H is sparse.”
3D Benchmark on Discretization Schemes for Anisotropic Diffusion Problems on General Grids (2008, methodology): “Written in ANSI/ISO C, UMFPACK is a set of routines for solving unsymmetric sparse linear systems Ax = b, using the Unsymmetric MultiFrontal method (see [17, 18] for details).”
Domain decomposition methods for advection dominated linear-quadratic elliptic optimal control problems (2005, methodology): “preconditioner, cf. (4.14)) exactly (up to floating point arithmetic) using UMFPACK 4.3 [ 8 ].”
Benchmark computations of diffuse interface models for two‐dimensional bubble dynamics (2012, methodology): “The linearized system was solved using the direct unsymmetric multifrontal method (UMFPACK, [21]).”