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.

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  1. Phillips, Edward G.; Shadid, John N.; Cyr, Eric C.; Elman, Howard C.; Pawlowski, Roger P.: Block preconditioners for stable mixed nodal and edge finite element representations of incompressible resistive MHD (2016)
  2. Gordon, Dan; Gordon, Rachel: Robust and highly scalable parallel solution of the Helmholtz equation with large wave numbers (2013)
  3. Filippone, Salvatore; Buttari, Alfredo: Object-oriented techniques for sparse matrix computations in Fortran 2003 (2012)
  4. Gordon, Dan; Gordon, Rachel: Parallel solution of high frequency Helmholtz equations using high order finite difference schemes (2012)
  5. Nishiura, Yasumasa; Teramoto, Takashi; Yuan, Xiaohui: Heterogeneity-induced spot dynamics for a three-component reaction-diffusion system (2012)
  6. D’Ambra, Pasqua; Di Serafino, Daniela; Filippone, Salvatore: MLD2P4: a package of parallel algebraic multilevel domain decomposition preconditioners in Fortran 95 (2010)
  7. Gordon, Dan; Gordon, Rachel: CARP-CG: A robust and efficient parallel solver for linear systems, applied to strongly convection dominated PDEs (2010)
  8. Gordon, Dan; Gordon, Rachel: Row scaling as a preconditioner for some nonsymmetric linear systems with discontinuous coefficients (2010)
  9. Lin, Paul T.; Shadid, John N.: Towards large-scale multi-socket, multicore parallel simulations: Performance of an MPI-only semiconductor device simulator (2010)
  10. Luisier, Mathieu; Klimeck, Gerhard: Numerical strategies towards peta-scale simulations of nanoelectronics devices (2010)
  11. Raghavan, Padma; Teranishi, Keita: Parallel hybrid preconditioning: incomplete factorization with selective sparse approximate inversion (2010)
  12. Shadid, J.N.; Pawlowski, R.P.; Banks, J.W.; Chacón, L.; Lin, P.T.; Tuminaro, R.S.: Towards a scalable fully-implicit fully-coupled resistive MHD formulation with stabilized FE methods (2010)
  13. Lin, Paul T.; Shadid, John N.; Sala, Marzio; Tuminaro, Raymond S.; Hennigan, Gary L.; Hoekstra, Robert J.: Performance of a parallel algebraic multilevel preconditioner for stabilized finite element semiconductor device modeling (2009)
  14. Padula, Anthony D.; Scott, Shannon D.; Symes, William W.: A software framework for abstract expression of coordinate-free linear algebra and optimization algorithms (2009)
  15. Gokarn, A.; Battaglia, F.; Fox, R.O.; Hill, J.C.; Reveillon, J.: Large eddy simulations of incompressible turbulent flows using parallel computing techniques (2008)
  16. Sala, Marzio; Spotz, William F.; Heroux, Michael A.: PyTrilinos: High-performance distributed-memory solvers for Python (2008)
  17. Sala, Marzio; Tuminaro, Raymond S.: A new Petrov-Galerkin smoothed aggregation preconditioner for nonsymmetric linear systems (2008)
  18. D’Ambra, Pasqua; di Serafino, Daniela; Filippone, Salvatore: On the development of PSBLAS-based parallel two-level Schwarz preconditioners (2007)
  19. Heroux, Michael A.; Salinger, Andrew G.; Frink, Laura J.D.: Parallel segregated Schur complement methods for fluid density functional theories (2007)
  20. 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)

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