TAUCS: a library of sparse linear solvers. The current version of the library (1.0) includes the following functionality: Multifrontal Supernodal Cholesky Factorization. This code is quite fast (several times faster than Matlab 6’s sparse Cholesky) but not completely state of the art. It uses the BLAS to factor and compute updates from fundamental supernodes, but it does not use relaxed supernodes. Left-Looking Supernodal Cholesky Factorization. Slower than the multifrontal solver but uses less memory. Drop-Tolerance Incomplete-Cholesky Factorization. Much slower than the supernodal solvers when it factors a matrix completely, but it can drop small elements from the factorization. It can also modify the diagonal elements to maintain row sums. The code uses a column-based left-looking approach with row lists. LDL^T Factorization. Column-based left-looking with row lists. Use the supernodal codes instead. Out-of-Core, Left-Looking Supernodal Sparse Cholesky Factorization. Solves huge systems by storing the Cholesky factors in files. Can work with factors whose size is tens of gigabytes on 32-bit machines with 32-bit file systems. Out-of-Core Sparse LU with Partial Pivoting Factor and Solve. Can solve huge unsymmetric linear systems. Ordering Codes and Interfaces to Existing Ordering Codes. The library includes a unified interface to several ordering codes, mostly existing ones. The ordering codes include Joseph Liu’s genmmd (a minimum-degree code in Fortran), Tim Davis’s amd codes (approximate minimum degree), Metis (a nested-dissection/minimum-degree code by George Karypis and Vipin Kumar), and a special-purpose minimum-degree code for no-fill ordering of tree-structured matrices. All of these are symmetric orderings. Matrix Operations. Matrix-vector multiplication, triangular solvers, matrix reordering. Matrix Input/Output. Routines to read and write sparse matrices using a simple file format with one line per nonzero, specifying the row, column, and value. Also routines to read matrices in Harwell-Boeing format. Matrix Generators. Routines that generate finite-differences discretizations of 2- and 3-dimensional partial differential equations. Useful for testing the solvers. Iterative Solvers. Preconditioned conjugate-gradients and preconditioned minres. Vaidya’s Preconditioners. Augmented Maximum-weight-basis preconditioners. These preconditioners work by dropping nonzeros from the coefficient matrix and them factoring the preconditioner directly. Recursive Vaidya’s Preconditioners. These preconditioners also drop nonzeros, but they don’t factor the resulting matrix completely. Instead, they eliminate rows and columns which can be eliminated without producing much fill. They then form the Schur complement of the matrix with respect to these rows and columns and drop elements from the Schur complement, and so on. During the preconditioning operation, we solve for the Schur complement elements iteratively. Multilevel-Support-Graph Preconditioners. Similar to domain-decomposition preconditioners. Includes the Gremban-Miller preconditioners. Utility Routines. Timers (wall-clock and CPU time), physical-memory estimator, and logging.

References in zbMATH (referenced in 26 articles , 2 standard articles )

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  1. Krauth, Niklas; Nieser, Matthias; Polthier, Konrad: Differential-based geometry and texture editing with brushes (2014)
  2. Becker, G.; Geuzaine, C.; Noels, L.: A one field full discontinuous Galerkin method for Kirchhoff-love shells applied to fracture mechanics (2011)
  3. Agullo, Emmanuel; Guermouche, Abdou; L’Excellent, Jean-Yves: Reducing the I/O volume in sparse out-of-core multifrontal methods (2010)
  4. Amestoy, P.; Duff, I.S.; Guermouche, A.; Slavova, Tz.: Analysis of the solution phase of a parallel multifrontal approach (2010)
  5. Li, Zheng; Levin, David; Deng, Zhengjie; Liu, Dingyuan; Luo, Xiaonan: Cage-free local deformations using Green coordinates (2010)
  6. Meng, Weiliang; Sheng, Bin; Lv, Weiwei; Sun, Hanqiu; Wu, Enhua: Differential geometry images: remeshing and morphing with local shape preservation (2010)
  7. Nayak, R.K.; Biswal, M.P.; Padhy, S.: Modification of Karmarkar’s projective scaling algorithm (2010)
  8. Avron, Haim; Chen, Doron; Shklarski, Gil; Toledo, Sivan: Combinatorial preconditioners for scalar elliptic finite-element problems (2009)
  9. Lai, Yu-Kun; Hu, Shi-Min; Martin, Ralph R.; Rosin, Paul L.: Rapid and effective segmentation of 3D models using random walks (2009)
  10. Lin, Yuxu; Chen, Chun; Song, Mingli; Liu, Zicheng: Dual-RBF based surface reconstruction (2009)
  11. Pan, Rongjiang; Meng, Xiangxu; Whangbo, Taegkeun: Hermite variational implicit surface reconstruction (2009)
  12. Boman, Erik G.; Hendrickson, Bruce; Vavasis, Stephen: Solving elliptic finite element systems in near-linear time with support preconditioners (2008)
  13. Koutsovasilis, Javier P.; Beitelschmidt, M.: Comparison of model reduction techniques for large mechanical systems (2008)
  14. Heim, S.; Fahrmeir, L.; Eilers, P.H.C.; Marx, B.D.: 3D space-varying coefficient models with application to diffusion tensor imaging (2007)
  15. Ribeiro, F.L.B.; Ferreira, I.A.: Parallel implementation of the finite element method using compressed data structures (2007)
  16. Masuda, Hiroshi; Yoshioka, Yasuhiro; Furukawa, Yoshiyuki: Preserving form-features in interactive mesh deformation (2006)
  17. Meshar, Omer; Irony, Dror; Toledo, Sivan: An out-of-core sparse symmetric-indefinite factorization method. (2006)
  18. Sharp, Richard; Machiraju, Raghu: Accelerating subsurface scattering using Cholesky factorization (2006)
  19. Xu, Dong; Chen, Wei; Zhang, Hongxin; Bao, Hujun: Multi-level differential surface representation based on local transformations (2006)
  20. Botsch, Mario; Bommes, David; Kobbelt, Leif: Efficient linear system solvers for mesh processing (2005)

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