S. F. Ashby and R. D. Falgout. A parallel multigrid preconditioned conjugate gradient algorithm for groundwater flow simulations. Nuclear Science and Engineering, 124(1):145–159, September 1996. Also available as LLNL Technical Report UCRL-JC-122359.


A. Baker, R. Falgout, T. Kolev, and U. M. Yang. Multigrid smoothers for ultra-parallel computing. SIAM J. on Sci. Comp., 33:2864–2887, 2011. Also available as LLNL technical report LLLNL-JRNL-473191.


A.H. Baker, R.D. Falgout, and U.M. Yang. An assumed partition algorithm for determining processor inter-communication. Parallel Computing, 32:394–414, 2006.


A. Baker, T. Kolev, and U. M. Yang. Improving algebraic multigrid interpolation operators for linear elasticity problems. Numer. Linear Algebra Appl., 17:495–517, 2010. Also available as LLNL technical report LLLNL-JRNL-412928.


Luc Berger-Vergiat, Brian Kelley, Sivasankaran Rajamanickam, Jonathan Hu, Katarzyna Swirydowicz, Paul Mullowney, Stephen Thomas, Ichitaro Yamazaki. Two-Stage Gauss–Seidel Preconditioners and Smoothers for Krylov Solvers on a GPU cluster.


BLOPEX, parallel preconditioned eigenvalue solvers.


P. N. Brown, R. D. Falgout, and J. E. Jones. Semicoarsening multigrid on distributed memory machines. SIAM J. Sci. Comput., 21(5):1823–1834, 2000. Special issue on the Fifth Copper Mountain Conference on Iterative Methods. Also available as LLNL technical report UCRL-JC-130720.


E. Chow. A priori sparsity patterns for parallel sparse approximate inverse preconditioners. SIAM J. Sci. Comput., 21:1804–1822, 2000.


R. L. Clay et al. An annotated reference guide to the Finite Element Interface (FEI) specification, Version 1.0. Technical Report SAND99-8229, Sandia National Laboratories, Livermore, CA, 1999.


CMake, a cross-platform open-source build system.


H. De Sterck, R. Falgout, J. Nolting, and U. M. Yang. Distance-two interpolation for parallel algebraic multigrid. Numer. Linear Algebra Appl., 15:115–139, 2008. Also available as LLNL technical report UCRL-JRNL-230844.


H. De Sterck, U. M. Yang, and J. Heys. Reducing complexity in parallel algebraic multigrid preconditioners. SIAM Journal on Matrix Analysis and Applications, 27:1019–1039, 2006. Also available as LLNL technical report UCRL-JRNL-206780.


R. D. Falgout and J. E. Jones. Multigrid on massively parallel architectures. In E. Dick, K. Riemslagh, and J. Vierendeels, editors, Multigrid Methods VI, volume 14 of Lecture Notes in Computational Science and Engineering, pages 101–107, Berlin, 2000. Springer. Proc. of the Sixth European Multigrid Conference held in Gent, Belgium, September 27-30, 1999. Also available as LLNL technical report UCRL-JC-133948.


R. D. Falgout, J. E. Jones, and U. M. Yang. The design and implementation of hypre, a library of parallel high performance preconditioners. In A. M. Bruaset and A. Tveito, editors, Numerical Solution of Partial Differential Equations on Parallel Computers, pages 267–294. Springer–Verlag, 2006. Also available as LLNL technical report UCRL-JRNL-205459.


R. D. Falgout, J. E. Jones, and U. M. Yang. Conceptual interfaces in hypre. Future Generation Computer Systems, 22:239–251, 2006. Special issue on PDE software. Also available as LLNL technical report UCRL-JC-148957.


Robert D. Falgout and Jacob B. Schroder. Non-galerkin coarse grids for algebraic multigrid. SIAM J. Sci. Comput., 36(3):309–334, 2014.


A. Grayver and Tz. Kolev. Large-scale 3D geoelectromagnetic modeling using parallel adaptive high-order finite element method. Geophysics, 80(6):E277–E291, 2015. Also available as LLNL technical report LLNL-JRNL-665742.


M. Griebel, B. Metsch, and M. A. Schweitzer. Coarse grid classification: A parallel coarsening scheme for algebraic multigrid methods. Numerical Linear Algebra with Applications, 13(2–3):193–214, 2006. Also available as SFB 611 preprint No. 225, Universität Bonn, 2005.


M. Griebel, B. Metsch, and M. A. Schweitzer. Coarse grid classification - Part II: Automatic coarse grid agglomeration for parallel AMG. Preprint No. 271, Sonderforschungsbereich 611, Universität Bonn, 2006.


V. E. Henson and U. M. Yang. BoomerAMG: a parallel algebraic multigrid solver and preconditioner. Applied Numerical Mathematics, 41(5):155–177, 2002. Also available as LLNL technical report UCRL-JC-141495.


R. Hiptmair and J. Xu. Nodal auxiliary space preconditioning in \(H(curl)\) and \(H(div)\) spaces. Numer. Math., 2006.


D. Hysom and A. Pothen. Efficient parallel computation of ILU(k) preconditioners. In Proceedings of Supercomputing ‘99. ACM, November 1999. Published on CDROM, ISBN #1-58113-091-0, ACM Order #415990, IEEE Computer Society Press Order # RS00197.


D. Hysom and A. Pothen. A scalable parallel algorithm for incomplete factor preconditioning. SIAM J. Sci. Comput., 22(6):2194–2215, 2001.


G. Karypis and V. Kumar. Parallel threshold-based ILU factorization. Technical Report 061, University of Minnesota, Department of Computer Science/Army HPC Research Center, Minneapolis, MN 5455, 1998.


A. Knyazev. Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method. SIAM J. Sci. Comput., 23(2):517–541, 2001.


A. Knyazev, I. Lashuk, M. Argentati, and E. Ovchinnikov. Block locally optimal preconditioned eigenvalue xolvers (blopex) in hypre and petsc. SIAM J. Sci. Comput., 25(5):2224–2239, 2007.


Tz. Kolev and P. Vassilevski. Parallel auxiliary space AMG for \(H(curl)\) problems. J. Comput. Math., 27:604–623, 2009. Special issue on Adaptive and Multilevel Methods in Electromagnetics. UCRL-JRNL-237306.


L. Yu. Kolotilina and A. Yu. Yeremin. Factorized Sparse Approximate Inverse Preconditionings I. Theory. SIAM J. Matrix Anal. A., 14(1):45–58, 1993.


R. Li, B. Sjogreen and U. M. Yang. A new class of AMG interpolation methods based on matrix-matrix multiplications. SIAM J. Sci. Comput., 43(5), S540–S564.


C. Janna, M. Ferronato, F. Sartoretto and G. Gambolati. FSAIPACK: A Software Package for High-Performance Factored Sparse Approximate Inverse Preconditioning. ACM T. Math. Software, 41(2):1–-26, 2015.


J. Jones and B. Lee. A multigrid method for variable coefficient maxwell’s equations. SIAM J. Sci. Comput., 27:1689–1708, 2006.


S. F. McCormick. Multilevel Adaptive Methods for Partial Differential Equations, volume 6 of Frontiers in Applied Mathematics. SIAM Books, Philadelphia, 1989.


J.E. Morel, Randy M. Roberts, and Mikhail J. Shashkov. A local support-operators diffusion discretization scheme for quadrilateral r-z meshes. J. Comp. Physics, 144:17–51, 1998.


V. A. Paludetto Magri, A. Franceschini and C. Janna. A novel algebraic multigrid approach based on adaptive smoothing and prolongation for ill-conditioned systems. SIAM J. Sci. Comput., 41(1):A190–A219, 2019.


J. W. Ruge and K. Stüben. Algebraic multigrid (AMG). In S. F. McCormick, editor, Multigrid Methods, volume 3 of Frontiers in Applied Mathematics, pages 73–130. SIAM, Philadelphia, PA, 1987.


S. Schaffer. A semi-coarsening multigrid method for elliptic partial differential equations with highly discontinuous and anisotropic coefficients. SIAM J. Sci. Comput., 20(1):228–242, 1998.


K. Stüben. Algebraic multigrid (AMG): an introduction with applications. In U. Trottenberg, C. Oosterlee, and A. Schüller, editors, Multigrid. Academic Press, 2001.


Umpire: Managing Heterogeneous Memory Resources.


P. Vaněk, J. Mandel, and M. Brezina. Algebraic multigrid based on smoothed aggregation for second and fourth order problems. Computing, 56:179–196, 1996.


P. Vaněk, M. Brezina, and J. Mandel. Convergence of algebraic multigrid based on smoothed aggregation. Numerische Mathematik, 88:559–579, 2001.


P. Vassilevski and U. M. Yang. Reducing communication in algebraic multigrid using additive variants. Numer. Linear Algebra Appl., 21:275–296, 2014. Also available as LLNL technical report LLLNL-JRNL-637872.


U. M. Yang. On the use of relaxation parameters in hybrid smoothers. Numerical Linear Algebra with Applications, 11:155–172, 2004.


U. M. Yang. Parallel algebraic multigrid methods - high performance preconditioners. In A. M. Bruaset and A. Tveito, editors, Numerical Solution of Partial Differential Equations on Parallel Computers, pages 209–236. Springer-Verlag, 2006. Also available as LLNL technical report UCRL-BOOK-208032.


U. M. Yang. On long range interpolation operators for aggressive coarsening. Numer. Linear Algebra Appl., 17:453–472, 2010. Also available as LLNL technical report LLLNL-JRNL-417371.