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. Hascoët, L.: A method for automatic placement of communications in SPMD parallelisation (2001)
  2. Lehoucq, Richard B.; Salinger, Andrew G.: Large-scale eigenvalue calculations for stability analysis of steady flows on massively parallel computers (2001)
  3. Bai, Zhaojun (ed.); Demmel, James (ed.); Dongarra, Jack (ed.); Ruhe, Axel (ed.); Van der Vorst, Henk (ed.): Templates for the solution of algebraic eigenvalue problems. A practical guide (2000)
  4. Cairncross, Richard A.; Schunk, P. Randall; Baer, Thomas A.; Rao, Rekha R.; Sackinger, Phillip A.: A finite element method for free surface flows of incompressible fluids in three dimensions. I: Boundary fitted mesh motion (2000)
  5. Douglas Frink, Laura J.; Salinger, Andrew G.: Two- and three-dimensional nonlocal density functional theory for inhomogeneous fluids. I: Algorithms and parallelization (2000)
  6. Drumm, C. R.; Lorenz, J.: Parallel FE approximation of the even/odd-parity form of the linear Boltzmann equation. (2000)
  7. Saad, Yousef; Sosonkina, Maria: Distributed Schur complement techniques for general sparse linear systems (2000)
  8. Wu, Kesheng; Simon, Horst: Thick-restart Lanczos method for large symmetric eigenvalue problems (2000)
  9. Christen, Peter: A parallel iterative linear system solver with dynamic load balancing (1999)
  10. Saad, Yousef; Sosonkina, Maria: Non-standard parallel solution strategies for distributed sparse linear systems (1999)
  11. Shadid, J. N.: A fully-coupled Newton-Krylov solution method for parallel unstructured finite element fluid flow, heat and mass transfer simulations (1999)
  12. van der Weide, E.; Deconinck, H.; Issman, E.; Degrez, G.: A parallel, implicit, multi-dimensional upwind, residual distribution method for the Navier-Stokes equations on unstructured grids (1999)
  13. Wu, Kesheng; Simon, Horst: A parallel Lanczos method for symmetric generalized eigenvalue problems (1999)
  14. Wyrzykowski, Roman; Sczygiol, Nobert; Olas, Tomasz; Kanevski, Juri: Parallel finite element modeling of solidification processes (1999)
  15. Pernice, Michael; Walker, Homer F.: NITSOL: A Newton iterative solver for nonlinear systems (1998)
  16. Saad, Yousef; Sosonkina, Maria; Zhang, Jun: Domain decomposition and multi-level type techniques for general sparse linear systems (1998)
  17. Balay, Satish; Gropp, William D.; McInnes, Lois Curfman; Smith, Barry F.: Efficient management of parallelism in object-oriented numerical software libraries (1997)
  18. Shadid, John; Hutchinson, Scott; Hennigan, Gary; Moffat, Harry; Devine, Karen: Efficient parallel computation of unstructured finite element reacting flow solutions (1997)
  19. Shadid, John N.; Tuminaro, Ray S.; Walker, Homer F.: An inexact Newton method for fully coupled solution of the Navier-Stokes equations with heat and mass transport (1997)