Publications




    If you are looking for the ML user guides, they can be found here.

  • M. Sala. An Object-Oriented Framework for the Development of Scalable Parallel Multilevel Preconditioners. ACM Transactions on Mathematical Software, 32 (3), 2006. (doi link)

  • Peter Arbenz, Harry van Lenthe, Uche Mennel, Ralph Muller, Marzio Sala. Multi-level $\mu$-Finite Element Analysis for Human Bone Structures. Submitted to the Proceeding of the PARA'06 conference, Umea, Sweden June 2006.

  • P. Lin, M. Sala, J. Shadid, and R. Tuminaro. Performance of Fully-Coupled Algebraic Multilevel Domain Decomposition Preconditioners for Incompressible Flow and Transport. Int. J. Numer. Meth. Engng, Vol. 67, Issue 2, p. 208-225, 2006. (doi link)

  • J.  Hu , R. Tuminaro , P. Bochev , C.   Garasi, and A.  Robinson. Toward an $h$-independent Algebraic Multigrid Method for Maxwell's Equations. Siam Journal on Scientific Computing, Vol. 27, Issue 5, p. 1669-1688, 2006. (doi link)

  • M. Sala, J. Shadid, and R. Tuminaro. An Improved Convergence Bound for Aggregation-Based Domain Decomposition Preconditioners. SIAM Journal on Matrix Analysis and Applications Vol. 27, Number 3 p. 744-756, 2005. (doi link)

  • M. Sala, P. Lin, R. Tuminaro, and J. Shadid. Algebraic Multilevel Preconditioners for non-symmetric PDEs on Stretched Grids. Proceeding of the 16th Domain Decomposition Conference, New York, USA, 2005. To appear in Springer Lecture Notes in Computational Science and Engineering.

  • H. Waisman, J. Fish, R. Tuminaro, and J. Shadid. Acceleration of the generalized global basis (GGB) method for nonlinear problems. Journal of Computational Physics, Vol. 210 (1), p. 274-291 , 2005. (doi link)

  • M. Sala. Analysis of Two-level Domain Decomposition Preconditioners Based on Aggregation. Mathematical Modelling and Numerical Analysis, Vol. 38 (5), p. 765--780, 2004. (doi link)

  • P. Bochev , C.   Garasi, J.  Hu , A Robinson and R. Tuminaro. An Improved Algebraic Multigrid Method for Solving Maxwell's Equations. Siam Journal on Scientific Computing, 25, 623-642, 2003. (paper, doi link)

  • C. Douglas, J.  Hu, J.  Ray, D. Thorne and R. Tuminaro. Cache Aware Multigrid for Variable Coefficient Elliptic Problems on Adaptive Mesh Refinement Hierarchies. Numer. Linear Algebra Appl., 11 (2-3), p. 173-187, 2004. (paper, doi link)

  • H. Waisman, J. Fish, R. Tuminaro, and J. Shadid. The Generalized Global Basis (GGB) Method. Int. J. Numer. Meth. Engng, Vol. 61 (8): 1243-1269, October 2004. (doi link)

  • L. Giraud, F. Guevara Vasquez, and R. Tuminaro. Grid transfer operators for highly variable coefficient problems in two-level non-overlapping domain decomposition methods. Numer. Linear Algebra Appl., 10, 467-484, 2003. (paper)

  • P. Bochev, J. Hu, A. Robinson, and R. Tuminaro. Towards robust 3D Z-pinch simulations: discretization and fast solvers for magnetic diffusion in heterogeneous conductors. Elec. Trans. Numer. Analysis, 15, 2003. (paper, journal)

  • M. Adams , M.  Brezina, J.  Hu and R. Tuminaro. Parallel Multigrid Smoothing: Polynomial versus Gauss-Seidel. JCP, Vol. 188 (2), 593-610 , 2003. (paper, doi link)

  • H. Elman, V.  Howle, J.  Shadid and R. Tuminaro. A Parallel Block Preconditioner for the Three-Dimensional Incompressible Navier-Stokes Equations. JCP, Vol. 187 (2), 504-523, 2003. (paper)

  • M.  Heroux, R.  Bartlett, V.  Howle, R.  Hoekstra, J.  Hu, T.  Kolda, R.  Lehoucq, K.  Long, R.  Pawlowski, E.  Phipps, A.  Salinger, H.  Thornquist, R.  Tuminaro, J.  Willenbring and A.  Williams. An Overview of Trilinos. Technical Report SAND2003-2927, Sandia National Laboratories, August 2003. (paper)

  • R. Tuminaro, H.  Walker, and J. Shadid. On backtracking failure in newton-gmres methods with a demonstration for the Navier-Stokes equations. JCP, Vol. 180 (2), p. 549-558, 2002. (doi link, paper)

  • R. Tuminaro, C. Tong, J. Shadid, K. Devine, and D. Day. On a multilevel preconditioning module for unstructured mesh Krylov solvers: Two-level Schwarz. Comm. Num. Meth. Eng., Vol. 18 (6), p. 363-389, 2002. (paper, doi link)

  • C. Douglas, J.  Hu, J.  Ray, D. Thorne and R. Tuminaro. Fast, Adaptively Refined Computational Elements in 3D in Computational Science - ICCS 2002, P. M. A. Sllot, C. J. K. Tan, J. J. Dongarra, and A. G. Hoekstra (eds.), 3 , p. 774-783, 2002. (paper)

  • R. Tuminaro and C. Tong. Parallel smoothed aggregation multigrid: Aggregation strategies on massively parallel machines. In J. Donnelley, editor, SuperComputing 2000 Proceedings, 2000. (paper, doi link)

  • C. Tong and R. S. Tuminaro. ML 2.0 smoothed aggregation user's guide. Technical Report SAND2001-8028, Sandia National Laboratories, December 2000. (paper)

  • R. Tuminaro, M. Heroux, S. Hutchinson, and J. Shadid. Official Aztec user's guide: Version 2.1. Technical Report Sand99-8801J, Sandia National Laboratories, Albuquerque NM, 87185, Nov 1999. (paper)