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. Burroughs, Elizabeth A.; Romero, Louis A.; Lehoucq, Richard B.; Salinger, Andrew G.: Linear stability of flow in a differentially heated cavity via large-scale eigenvalue calculations (2004)
  2. Knoll, D. A.; Keyes, D. E.: Jacobian-free Newton-Krylov methods: a survey of approaches and applications. (2004)
  3. Messmer, Peter; Bruhwiler, David L.: A parallel electrostatic solver for the VORPAL code (2004)
  4. Ober, Curtis C.; Shadid, John N.: Studies on the accuracy of time-integration methods for the radiation-diffusion equations (2004)
  5. Seoane, Natalia; García-Loureiro, A. J.: Analysis of parallel numerical libraries to solve the 3D electron continuity equation (2004)
  6. Xu, Shuting; Zhang, Jun: A parallel hybrid web document clustering algorithm and its performance study (2004)
  7. Davis, Justin R.; Sheng, Y. Peter: Development of a parallel storm surge model (2003)
  8. Sears, Mark P.; Frink, Laura J. D.: A new efficient method for density functional theory calculations of inhomogeneous fluids. (2003)
  9. Arnold, Dorian C.; Casanova, Henri; Dongarra, Jack: Innovations of the NetSolve Grid Computing System (2002)
  10. Fang, Z.; Ingber, M. S.; Martinez, M. J.: The solution of magnetostatic BEM systems of equations using iterative methods. (2002)
  11. Keyes, David E.: Terascale implicit methods for partial differential equations (2002)
  12. Oliker, Leonid; Li, Xiaoye; Husbands, Parry; Biswas, Rupak: Effects of ordering strategies and programming paradigms on sparse matrix computations (2002)
  13. Saad, Y.; Sosonkina, M.: pARMS: A package for solving general sparse linear systems on parallel computers (2002)
  14. Sala, Marzio: An algebraic 2-level domain decomposition preconditioner with applications to the compressible Euler equations (2002)
  15. Salinger, Andrew G.; Lehoucq, Richard B.; Pawlowski, Roger P.; Shadid, John N.: Computational bifurcation and stability studies of the 8:1 thermal cavity problem (2002)
  16. Shen, Chi; Zhang, Jun: Parallel two level block ILU preconditioning techniques for solving large sparse linear systems (2002)
  17. Tuminaro, Raymond S.; Walker, Homer F.; Shadid, John N.: On backtracking failure in Newton-GMRES methods with a demonstration for the Navier-Stokes equations (2002)
  18. Day, David; Heroux, Michael A.: Solving complex-valued linear systems via equivalent real formulations (2001)
  19. Deng, G. B.; Piquet, J.; Vasseur, X.; Visonneau, M.: A new fully coupled method for computing turbulent flows (2001)
  20. Elmroth, Erik; Ding, Chris; Wu, Yu-Shu: High performance computations for large scale simulations of subsurface multiphase fluid and heat flow (2001)