Aztec

Aztec is a library that provides algorithms for the iterative solution of large sparse linear systems arising in scientific and engineering applications. It is a stand-alone package comprising a set of iterative solvers, preconditioners and matrix-vector multiplication routines. Users are not required to provide their own matrix-vector multiplication routines or preconditioners in order to solve a linear system. The Aztec library is written in C and is also callable from Fortran. Overall, the package was designed to be portable and easy to use. The user may input the linear system in a simple format and Aztec will perform the necessary transformations for the matrix-vector multiplication and preconditioning. After the transformations, the iterative solvers can run efficiently. If the input matrix is suitably partitioned, the efficiency can be further enhanced. The major components of Aztec are implementations of iterative solvers (CG, CGS, BiCGSTAB, GMRES and TFQMR) and preconditioners (point Jacobi, block Jacobi, Gauss-Seidel, least-squares polynomials, and overlapping domain decomposition using sparse LU, ILU, ILUT, BILU and ICC within domains). Aztec supports two different sparse matrix notations: a) a point-entry modified sparse row (MSR) format; b) a block-entry variable block row (VBR) format. These two formats have been generalized for parallel implementation and the library includes highly optimized matrix-vector multiply kernels and preconditioners for both types of data structures.


References in zbMATH (referenced in 79 articles )

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  1. Sala, Marzio; Spotz, William F.; Heroux, Michael A.: PyTrilinos: High-performance distributed-memory solvers for Python (2008)
  2. Sala, Marzio; Tuminaro, Raymond S.: A new Petrov-Galerkin smoothed aggregation preconditioner for nonsymmetric linear systems (2008)
  3. Wall, Wolfgang A.; Rabczuk, Timon: Fluid-structure interaction in lower airways of CT-based lung geometries (2008)
  4. D’Ambra, Pasqua; di Serafino, Daniela; Filippone, Salvatore: On the development of PSBLAS-based parallel two-level Schwarz preconditioners (2007)
  5. Heroux, Michael A.; Salinger, Andrew G.; Frink, Laura J. D.: Parallel segregated Schur complement methods for fluid density functional theories (2007)
  6. Läuter, Matthias; Handorf, Dörthe; Rakowsky, Natalja; Behrens, Jörn; Frickenhaus, Stephan; Best, Meike; Dethloff, Klaus; Hiller, Wolfgang: A parallel adaptive barotropic model of the atmosphere (2007)
  7. Vladimirova, Natalia: Model flames in the Boussinesq limit: sising bubbles (2007)
  8. Lin, Paul T.; Sala, Marzio; Shadid, John N.; Tuminaro, Ray S.: Performance of fully coupled algebraic multilevel domain decomposition preconditioners for incompressible flow and transport (2006)
  9. Martinez, M. J.: Comparison of Galerkin and control volume finite element for advection-diffusion problems (2006)
  10. Pawlowski, R. P.; Salinger, A. G.; Shadid, J. N.; Mountziaris, T. J.: Bifurcation and stability analysis of laminar isothermal counterflowing jets (2006)
  11. Seoane, Natalia; García-Loureiro, Antonio J.: Study of parallel numerical methods for semiconductor device simulation (2006)
  12. Shadid, J. N.; Salinger, A. G.; Pawlowski, R. P.; Lin, P. T.; Hennigan, G. L.; Tuminaro, R. S.; Lehoucq, R. B.: Large-scale stabilized FE computational analysis of nonlinear steady-state transport/reaction systems (2006)
  13. Burroughs, E. A.; Coutsias, E. A.; Romero, L. A.: A reduced-order partial differential equation model for the flow in a thermosyphon (2005)
  14. Frayssé, Valéire; Giraud, Luc; Gratton, Serge; Langou, Julien: Algorithm 842: A set of GMRES routines for real and complex arithmetics on high performance computers (2005)
  15. Gee, Michael; Ramm, Ekkehard; Wall, Wolfgang A.: Parallel multilevel solution of nonlinear shell structures (2005)
  16. Gordon, Dan; Gordon, Rachel: Component-averaged row projections: a robust, block-parallel scheme for sparse linear systems (2005)
  17. Heroux, Michael A.; Bartlett, Roscoe A.; Howle, Vicki E.; Hoekstra, Robert J.; Hu, Jonathan J.; Kolda, Tamara G.; Lehoucq, Richard B.; Long, Kevin R.; Pawlowski, Roger P.; Phipps, Eric T.; Salinger, Andrew G.; Thornquist, Heidi; Tuminaro, Ray S.; Willenbring, James M.; Williams, Alan; Stanley, Kendall S.: An overview of the Trilinos project. (2005)
  18. Salinger, A. G.; Burroughs, E. A.; Pawlowski, R. P.; Phipps, E. T.; Romero, L. A.: Bifurcation tracking algorithms and software for large scale applications (2005)
  19. Shadid, J. N.; Tuminaro, R. S.; Devine, K. D.; Hennigan, G. L.; Lin, P. T.: Performance of fully coupled domain decomposition preconditioners for finite element transport/reaction simulations (2005)
  20. Wingate, David; Seppi, Kevin D.: Prioritization methods for accelerating MDP solvers (2005)