Trilinos: Enabling Scientific Computing across Diverse Hardware Architectures at Scale

[en] Trilinos is a community-developed, open-source software framework that facilitates building large-scale, complex, multiscale, multiphysics simulation code bases for scientific and engineering problems. Since the Trilinos framework has undergone substantial changes to support new applications and new hardware architectures, this document is an update to “An Overview of the Trilinos project” by Heroux et al. (ACM Transactions on Mathematical Software, 31(3):397–423, 2005). It describes the design of Trilinos, introduces its new organization in product areas, and highlights established and new features available in Trilinos. Particular focus is put on the modernized software stack based on the Kokkos ecosystem to deliver performance portability across heterogeneous hardware architectures. This article also outlines the organization of the Trilinos community and the contribution model to help onboard interested users and contributors.

Disciplines :

Computer science

Author, co-author :

Mayr, Matthias ; Institute for Mathematics and Computer-Based Simulation, Universität der Bundeswehr München, Neubiberg, Germany and Data Science & Computing Lab, Universität der Bundeswehr München, Neubiberg, Germany

Heinlein, Alexander ; Delft Institute of Applied Mathematics (DIAM), Delft University of Technology, Delft, Netherlands

Glusa, Christian ; Sandia National Laboratories, Albuquerque, New Mexico, USA

Rajamanickam, Sivasankaran ; Sandia National Laboratories, Albuquerque, New Mexico, USA

Arnst, Maarten ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Computational and stochastic modeling

Bartlett, Roscoe A. ; Sandia National Laboratories, Albuquerque, New Mexico, USA

Berger-Vergiat, Luc ; Sandia National Laboratories, Albuquerque, New Mexico, USA

Bowman, Erik G. ; Sandia National Laboratories, Albuquerque, New Mexico, USA

Devine, Karen ; Retired, Starkville, Mississippi, USA

Harper, Graham ; Sandia National Laboratories, Albuquerque, New Mexico, USA

More authors (23 more)

Language :

English

Title :

Trilinos: Enabling Scientific Computing across Diverse Hardware Architectures at Scale

Publication date :

08 June 2026

Journal title :

ACM Transactions on Mathematical Software

ISSN :

0098-3500

Publisher :

Association for Computing Machinery (ACM)

Volume :

Issue :

Pages :

1-34

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://dl.acm.org/doi/pdf/10.1145/3802822

Name of the research project :

U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Scientific Discovery through Advanced Computing

Funders :

NNSA - National Nuclear Security Administration
DOE - United States. Department of Energy
SNL - Sandia National Laboratories
EU - European Union

Funding text :

Laboratory Directed Research and Development program at Sandia National Laboratories; dtec.bw—Digitalization and Technology Research Center of the Bundeswehr; European Union—NextGenerationEU

Available on ORBi :

since 05 July 2026

Statistics

Number of views

11 (2 by ULiège)

Number of downloads

36 (1 by ULiège)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

OpenAlex citations

Bibliography

GitHub. 2024. FROSch Demo. Retrieved December 06, 2024 from https://github.com/searhein/frosch-demo
Sandia National Laboratories. 2024. Rapid Optimization Library (ROL). Retrieved December 06, 2024 from https://rol.sandia.gov
Ahmad Abdelfattah, Timothy Costa, Jack Dongarra, Mark Gates, Azzam Haidar, Sven Hammarling, Nicholas J. Higham, Jakub Kurzak, Piotr Luszczek, Stanimire Tomov, et al. 2021. A set of batched basic linear algebra subprograms and LAPACK routines. ACM Transactions on Mathematical Software 47, 3, Article 21 (June 2021), 23 pages. DOI: 10.1145/3431921
Seher Acer, Erik G. Boman, Christian A. Glusa, and Sivasankaran Rajamanickam. 2021. Sphynx: A parallel multi-GPU graph partitioner for distributed-memory systems. Parallel Computing 106 (2021), 102769. DOI: 10.1016/j.parco.2021.102769
Filipe A. C. S. Alves, Alexander Heinlein, and Hadi Hajibeygi. 2024. A computational study of algebraic coarse spaces for two-level overlapping additive Schwarz preconditioners. arXiv:2408.08187. Retrieved from https://arxiv.org/abs/2408.08187
Harbir Antil, Drew P. Kouri, and Denis Ridzal. 2023. ALESQP: An augmented Lagrangian equality-constrained SQP method for optimization with general constraints. SIAM Journal on Optimization 33, 1 (2023), 237–266. DOI: 10.1137/20M1378399
Harbir Antil, Drew P. Kouri, Denis Ridzal, David B. Robinson, and Maher Salloum. 2024. Uniform flow in axisymmetric devices through permeability optimization. Optimization and Engineering 25, 2 (2024), 669–697. DOI: 10.1007/s11081-023-09820-0
Wilkins Aquino, Gregory Bunting, Scott T. Miller, and Timothy F. Walsh. 2019. A gradient-based optimization approach for the detection of partially connected surfaces using vibration tests. Computer Methods in Applied Mechanics and Engineering 345 ( 2019), 323–335. DOI: 10.1016/j.cma.2018.11.002
Daniel Arndt, Wolfgang Bangerth, Maximilian Bergbauer, Marco Feder, Marc Fehling, Johannes Heinz, Timo Heister, Luca Heltai, Martin Kronbichler, Matthias Maier, et al. 2023. The deal.II library, version 9.5. Journal of Numerical Mathematics 31, 3 (2023), 231–246. DOI: 10.1515/jnma-2023-0089
Brett W. Bader. 2005. Tensor-Krylov methods for solving large-scale systems of nonlinear equations. SIAM Journal on Numerical Analysis 43, 3 (2005), 1321–1347. DOI: 10.1137/040607095
Chris Baker, Erik Boman, Mike Heroux, Eric Keiter, Siva Rajamanickam, Rich Schiek, and Heidi Thornquist. 2012. Enabling next-generation parallel circuit simulation with Trilinos. In Euro-Par 2011: Parallel Processing Workshops. Michael Alexander, Pasqua D’Ambra, Adam Belloum, George Bosilca, Mario Cannataro, Marco Danelutto, Beniamino Di Martino, Michael Gerndt, Emmanuel Jeannot, Raymond Namyst, et al. (Eds.), Springer, Berlin, 315–323. DOI: 10.1007/978-3-642-29737-3_36
C. G. Baker and M. A. Heroux. 2012. Tpetra, and the use of generic programming in scientific computing. Scientific Programming 20, 2 (2012), 115–128. DOI: 10.3233/SPR-2012-0349
C. G. Baker, U. L. Hetmaniuk, R. B. Lehoucq, and H. K. Thornquist. 2009. Anasazi software for the numerical solution of large-scale eigenvalue problems. ACM Transactions on Mathematical Software 36, 3, Article 13 (July 2009), 23 pages. DOI: 10.1145/1527286.1527287
Satish Balay, Shrirang Abhyankar, Mark F. Adams, Jed Brown, Peter Brune, Kris Buschelman, Lisandro Dalcin, Alp Dener, Victor Eijkhout, William D. Gropp, et al. 2021. PETSc Web Page. Retrieved from https://www.mcs.anl.gov/petsc
Daniel Balzani, Alexander Heinlein, Axel Klawonn, Jascha Knepper, Sharan Nurani Ramesh, Oliver Rheinbach, Lea Saßmannshausen, and Klemens Uhlmann. 2024. A computational framework for pharmaco-mechanical interactions in arterial walls using parallel monolithic domain decomposition methods. GAMM-Mitteilungen 47, 1 (2024), e202370002. DOI: 10.1002/gamm.202370002
Robert J. Baraldi and Drew P. Kouri. 2023. A proximal trust-region method for nonsmooth optimization with inexact function and gradient evaluations. Mathematical Programming 201, 1–2 (2023), 559–598.
Igor A. Baratta, Joseph P. Dean, Jørgen S. Dokken, Michal Habera, Jack S. Hale, Chris N. Richardson, Marie E. Rognes, Matthew W. Scroggs, Nathan Sime, and Garth N. Wells. 2023. DOLFINx: The next generation FEniCS problem solving environment. Zenodo. DOI: 10.5281/zenodo.10447666
Roscoe A. Bartlett. 2007. Thyra Linear Operators and Vectors. Technical Report SAND2007-5984. Sandia National Laboratories.
Roscoe A. Bartlett. 2010. Teuchos C++ Memory Management Classes, Idioms, and Related Topics, the Complete Reference: A Comprehensive Strategy for Safe and Efficient Memory Management in C++ for High Performance Computing. Technical Report SAND2023-12265. Sandia National Laboratories. DOI: 10.2172/992335
Roscoe A. Bartlett. 2014. TriBITS Developers Guide and Reference. Technical Report CASL-U-2014-0075000b. Oak Ridge National Laboratory.
Roscoe A. Bartlett, Bart G. Van Bloemen Waanders, and Michael A. Heroux. 2004. Vector reduction/transformation operators. ACM Transactions on Mathematical Software 30, 1 (2004), 62–85. DOI: 10.1145/974781.974785
Eric Bavier, Mark Hoemmen, Sivasankaran Rajamanickam, and Heidi Thornquist. 2012. Amesos2 and Belos: Direct and iterative solvers for large sparse linear systems. Scientific Programming 20, 3 (2012), 241–255. DOI: 10.3233/SPR-2012-0352
Amir Beck. 2017. First-Order Methods in Optimization. SIAM.
Luc Berger-Vergiat, Christian A. Glusa, Graham Harper, Jonathan J. Hu, Matthias Mayr, Andrey Prokopenko, Christopher M. Siefert, Raymond S. Tuminaro, and Tobias A. Wiesner. 2023. MueLu User’s Guide. Technical Report SAND2023-12265. Sandia National Laboratories, Albuquerque, NM.
Matthew T. Bettencourt, Dominic A. S. Brown, Keith L. Cartwright, Eric C. Cyr, Christian A. Glusa, Paul T. Lin, Stan G. Moore, Duncan A. O. McGregor, Roger Pawlowski, Edward G. Phillips, et al. 2021. EMPIRE-PIC: A performance portable unstructured particle-in-cell code. Communications in Computational Physics 30, 4 (2021), 1232–1268. DOI: 10.4208/cicp.OA-2020-0261
P. Bochev, H. C. Edwards, R. C. Kirby, K. Peterson, and D. Ridzal. 2012. Solving PDEs with intrepid. Scientific Programming 20 (2012), 151–180. DOI: 10.3233/SPR-2012-0340
Pavel B. Bochev, Jonathan J. Hu, Christopher M. Siefert, and Raymond S. Tuminaro. 2008. An algebraic multigrid approach based on a compatible gauge reformulation of Maxwell’s equations. SIAM Journal on Scientific Computing 31, 1 (2008), 557–583.
Ian Bogle, Erik G. Boman, Karen Devine, Sivasankaran Rajamanickam, and George M. Slota. 2020. Distributed memory graph coloring algorithms for multiple GPUs. In 2020 IEEE/ACM 10th Workshop on Irregular Applications: Architectures and Algorithms (IA3), 54–62. DOI: 10.1109/IA351965.2020.00013
Erik G. Boman, Ümit V. Çatalyürek, Cédric Chevalier, and Karen D. Devine. 2012. The Zoltan and Isorropia parallel toolkits for combinatorial scientific computing: Partitioning, ordering and coloring. Scientific Programming 20, 2 (2012), 129–150. DOI: 10.3233/SPR-2012-0342
J. Bonilla, J. N. Shadid, X.-Z. Tang, M. M. Crockatt, P. Ohm, E. G. Phillips, R. P. Pawlowski, S. Conde, and O. Beznosov. 2023. On a fully-implicit VMS-stabilized FE formulation for low Mach number compressible resistive MHD with application to MCF. Computer Methods in Applied Mechanics and Engineering 417 ( 2023), 116359. DOI: 10.1016/j.cma.2023.116359
Joshua D. Booth, Nathan D. Ellingwood, Heidi K. Thornquist, and Sivasankaran Rajamanickam. 2017. Basker: Parallel sparse LU factorization utilizing hierarchical parallelism and data layouts. Parallel Computing 68 ( 2017), 17–31. DOI: 10.1016/j.parco.2017.06.003
Gregory Bunting, Scott T. Miller, Timothy F. Walsh, Clark R. Dohrmann, and Wilkins Aquino. 2021. Novel strategies for modal-based structural material identification. Mechanical Systems and Signal Processing 149 ( 2021), 107295. DOI: 10.1016/j.ymssp.2020.107295
Todd S. Coffey, C. T. Kelley, and David E. Keyes. 2003. Pseudotransient continuation and differential-algebraic equations. SIAM Journal on Scientific Computing 25, 2 (2003), 553–569. DOI: 10.1137/S106482750241044X
Paul G. Constantine, Eric T. Phipps, and Timothy M. Wildey. 2014. Efficient uncertainty propagation for network multiphysics systems. International Journal for Numerical Methods in Engineering 99, 3 (2014), 183–202.
Michael M. Crockatt, Sibusiso Mabuza, John N. Shadid, Sidafa Conde, Thomas M. Smith, and Roger P. Pawlowski. 2022. An implicit monolithic AFC stabilization method for the CG finite element discretization of the fully-ionized ideal multifluid electromagnetic plasma system. Journal of Computational Physics 464 ( 2022), 111228. DOI: 10.1016/j.jcp.2022.111228
Eric C. Cyr, John N. Shadid, and Raymond S. Tuminaro. 2012. Stabilization and scalable block preconditioning for the Navier–Stokes equations. Journal of Computational Physics 231, 2 (2012), 345–363. DOI: 10.1016/j.jcp.2011.09.001
Eric C. Cyr, John N. Shadid, and Raymond S. Tuminaro. 2016. Teko: A block preconditioning capability with concrete example applications in Navier–Stokes and MHD. SIAM Journal on Scientific Computing 38, 5 (2016), S307–S331. DOI: 10.1137/15M1017946
Timothy A. Davis and Ekanathan Palamadai Natarajan. 2010. Algorithm 907: KLU, a direct sparse solver for circuit simulation problems. ACM Transactions on Mathematical Software 37, 3 (2010), 1–17. DOI: 10.1145/1824801.1824814
Leszek Demkowicz, Jason Kurtz, David Pardo, Maciej Paszynski, Waldemar Rachowicz, and Adam Zdunek. 2007. Computing with Hp-Adaptive Finite Elements, Vol. 2: Frontiers Three Dimensional Elliptic and Maxwell Problems with Applications (1st ed.). Chapman & Hall/CRC.
Mehmet Deveci, Karen D. Devine, Kevin Pedretti, Mark A. Taylor, Sivasankaran Rajamanickam, and Ümit V. Çatalyürek. 2019. Geometric mapping of tasks to processors on parallel computers with mesh or torus networks. IEEE Transactions on Parallel and Distributed Systems 30, 9 (2019), 2018–2032. DOI: 10.1109/TPDS.2019.2900043
Mehmet Deveci, Sivasankaran Rajamanickam, Karen D. Devine, and Ümit V. Çatalyürek. 2016. Multi-Jagged: A scalable parallel spatial partitioning algorithm. IEEE Transactions on Parallel and Distributed Systems 27, 3 (2016), 803–817. DOI: 10.1109/TPDS.2015.2412545
Mehmet Deveci, Christian Trott, and Sivasankaran Rajamanickam. 2018. Multithreaded sparse matrix-matrix multiplication for many-core and GPU architectures. Parallel Computing 78 (2018), 33–46.
Clark R. Dohrmann, Axel Klawonn, and Olof B. Widlund. 2008. Domain decomposition for less regular subdomains: Overlapping schwarz in two dimensions. SIAM Journal on Numerical Analysis 46, 4 (2008), 2153–2168. DOI: 10.1137/070685841
H. Carter Edwards, Daniel Sunderland, Vicki Porter, Chris Amsler, and Sam Mish. 2012. Manycore performance-portability: Kokkos multidimensional array library. Scientific Programming 20, 2 (2012), 89–114. DOI: 10.3233/SPR-2012-0343
H. Carter Edwards, Christian R. Trott, and Daniel Sunderland. 2014. Kokkos: Enabling manycore performance portability through polymorphic memory access patterns. Journal of Parallel and Distributed Computing 74, 12 (2014), 3202–3216. DOI: 10.1016/j.jpdc.2014.07.003
Max Firmbach, Ivo Steinbrecher, Alexander Popp, and Matthias Mayr. 2024. An approximate block factorization preconditioner for mixed-dimensional beam-solid interaction. Computer Methods in Applied Mechanics and Engineering 431 ( 2024), 117256. DOI: 10.1016/j.cma.2024.117256
Federico Fuentes, Brendan Keith, Leszek Demkowicz, and Sriram Nagaraj. 2015. Orientation embedded high order shape functions for the exact sequence elements of all shapes. Computers & Mathematics with Applications 70, 4 (2015), 353–458. DOI: 10.1016/j.camwa.2015.04.027
Jan Niklas Fuhg, Reese Edward Jones, and Nikolaos Bouklas. 2024. Extreme sparsification of physics-augmented neural networks for interpretable model discovery in mechanics. Computer Methods in Applied Mechanics and Engineering 426 ( 2024), 116973.
Jérémie Gaidamour, Jonathan Hu, Chris Siefert, and Ray Tuminaro. 2012. Design considerations for a flexible multigrid preconditioning library. Scientific Programming 20, 3 (2012), 223–239. DOI: 10.3233/SPR-2012-0344
Michael W. Gee, Christopher M. Siefert, Jonathan J. Hu, Ray S. Tuminaro, and Marzio G. Sala. 2006. ML 5.0 Smoothed Aggregation User’s Guide. Technical Report SAND2006-2649. Sandia National Laboratories, Albuquerque, NM.
Roger G. Ghanem and Pol D. Spanos. 1990. Polynomial chaos in stochastic finite elements. Journal of Applied Mechanics 57, 1 (1990), 197–202. DOI: 10.1115/1.2888303
Roger G. Ghanem and Pol D. Spanos. 2003. Stochastic Finite Elements: A Spectral Approach. Courier Corporation.
P. Ghysels and W. Vanroose. 2014. Hiding global synchronization latency in the preconditioned conjugate gradient algorithm. Parallel Computing 40, 7 (2014), 224–238. DOI: 10.1016/j.parco.2013.06.0017
M. S. Gockenbach and W. W. Symes. 1996. Hilbert class library: A library of abstract C++ classes for optimization and inversion. Computers & Mathematics with Applications 32, 6 (1996), 1–13. DOI: 10.1016/0898-1221(96)00140-X
B. J. Gross, N. Trask, P. Kuberry, and P. J. Atzberger. 2020. Meshfree methods on manifolds for hydrodynamic flows on curved surfaces: A Generalized Moving Least-Squares (GMLS) approach. Journal of Computational Physics 409 (2020), 109340. DOI: 10.1016/j.jcp.2020.109340
David A. Ham, Paul H. J. Kelly, Lawrence Mitchell, Colin J. Cotter, Robert C. Kirby, Koki Sagiyama, Nacime Bouziani, Thomas J. Gregory, Jack Betteridge, Daniel R. Shapero, et al. 2023. Firedrake User Manual (1st ed.). Imperial College London, University of Oxford, Baylor University, and University of Washington. DOI: 10.25561/104839
Matthias Heinkenschloss and Luís N. Vicente. 1999. An interface between optimization and application for the numerical solution of optimal control problems. ACM Transactions on Mathematical Software 25, 2 (1999), 157–190. DOI: 10.1145/317275.317278
Alexander Heinlein, Christian Hochmuth, and Axel Klawonn. 2019. Monolithic overlapping schwarz domain decomposition methods with GDSW coarse spaces for incompressible fluid flow problems. SIAM Journal on Scientific Computing 41, 4 (2019), C291–C316. DOI: 10.1137/18M1184047
Sebastian Kinnewig, Alexander Heinlein, and Thomas Wick. 2025. Coupling deal.II and FROSch: A sustainable and accessible (O)RAS preconditioner. ACM Transactions on Mathematical Software 51, 4, Article 22 (2025), 1–29. DOI: 10.1145/3766906
Alexander Heinlein, Axel Klawonn, Jascha Knepper, and Oliver Rheinbach. 2019. Adaptive GDSW coarse spaces for overlapping schwarz methods in three dimensions. SIAM Journal on Scientific Computing 41, 5 (2019), A3045–A3072. DOI: 10.1137/18M1220613
Alexander Heinlein, Axel Klawonn, Jascha Knepper, and Lea Saß Mannshausen. 2026. Monolithic and Block Overlapping Schwarz Preconditioners for the Incompressible Navier—Stokes Equations. Electronic Transactions on Numerical Analysis (ETNA).
Alexander Heinlein, Axel Klawonn, Sivasankaran Rajamanickam, and Oliver Rheinbach. 2020. FROSch: A fast and robust overlapping Schwarz domain decomposition preconditioner based on Xpetra in Trilinos. In Domain Decomposition Methods in Science and Engineering XXV. Lecture Notes in Computational Science and Engineering, Vol. 138, Springer, Cham, 176–184. DOI: 10.1007/978-3-030-56750-7_19
Alexander Heinlein, Axel Klawonn, and Oliver Rheinbach. 2016. A parallel implementation of a two-level overlapping schwarz method with energy-minimizing coarse space based on Trilinos. SIAM Journal on Scientific Computing 38, 6 (2016), C713–C747. DOI: 10.1137/16M1062843
Alexander Heinlein, Axel Klawonn, Oliver Rheinbach, and Olof B. Widlund. 2018. Improving the parallel performance of overlapping Schwarz methods by using a smaller energy minimizing coarse space. In Domain Decomposition Methods in Science and Engineering XXIV. Lecture Notes in Computational Science and Engineering, Vol. 125, Springer, Cham, 383–392. DOI: 10.1007/978-3-319-93873-8_3
Alexander Heinlein, Mauro Perego, and Sivasankaran Rajamanickam. 2022. FROSch preconditioners for land ice simulations of Greenland and Antarctica. SIAM Journal on Scientific Computing 44, 2 (2022), B339–B367. DOI: 10.1137/21M1395260
Alexander Heinlein, Oliver Rheinbach, and Friederike Röver. 2022. Parallel scalability of three-level FROSch preconditioners to 220000 cores using the theta supercomputer. SIAM Journal on Scientific Computing 45, 3 (Aug. 2022), S173–S198. DOI: 10.1137/21M1431205
M. A. Heroux. 2004. AztecOO User Guide. Technical Report SAND2004-3796. Sandia National Laboratories, Albuquerque, NM.
Michael Allen Heroux. 2011. Toward Portable Programming of Numerical Linear Algebra on Manycore Nodes. Technical Report SAND20113556C Sandia National Lab.(SNL-NM), Albuquerque, NM. Retrieved from https://www.osti.gov/servlets/purl/1109301
Michael A. Heroux, Roscoe A. Bartlett, Vicki E. Howle, Robert J. Hoekstra, Jonathan J. Hu, Tamara G. Kolda, Lehoucq, Kevin R. Long, Roger P. Pawlowski, Eric T. Phipps, Andrew G. Salinger, et al. 2005. An overview of the Trilinos project. ACM Transactions on Mathematical Software 31, 3 (2005), 397–423. DOI: 10.1145/1089014.1089021
Michael A. Heroux and Damian Rouson. 2012. Special issue on the Trilinos project, part 1 of 2. Scientific Programming 20, 2 (2012), 104210. DOI: 10.3233/SPR-2012-0356
Michael A. Heroux and Damian Rouson. 2012. Special issue on the Trilinos project, part 2 of 2. Scientific Programming 20, 3 (2012), 513437. DOI: 10.3233/SPR-2012-0357
Michael A. Heroux and James M. Willenbring. 2012. A new overview of the Trilinos project. Scientific Programming 20, 2 (2012), 408130. DOI: 10.3233/SPR-2012-0355
Ralf Hiptmair. 1997. Multigrid method for H(div) in three dimensions. Electronic Transactions on Numerical Analysis 6 (1997), 133–152.
Mark Hoemmen. 2015. Tpetra Project Overview. In HPCOR Workshop. Retrieved from https://www.osti.gov/biblio/1307283
M. J. Hoffman, M. Perego, S. F. Price, W. H. Lipscomb, T. Zhang, D. Jacobsen, I. Tezaur, A. G. Salinger, R. Tuminaro, and L. Bertagna. 2018. MPAS-Albany land ice (MALI): A variable-resolution ice sheet model for earth system modeling using Voronoi grids. Geoscientific Model Development 11, 9 (2018), 3747–3780. DOI: 10.5194/gmd-11-3747-2018
Victoria E. Howle, Robert C. Kirby, Kevin Long, Brian Brennan, and Kimberly Kennedy. 2012. Playa: High-performance programmable linear algebra. Scientific Programming 20, 3 (2012), 257–273. DOI: 10.3233/SPR-2012-0347
A. Javeed, D. P. Kouri, D. Ridzal, and G. Von Winckel. 2022. Get ROL-ing: An introduction to sandia’s rapid optimization library. In 7th International Conference on Continuous Optimization.
Christian Kanzow and Theresa Lechner. 2021. Globalized inexact proximal newton-type methods for nonconvex composite functions. Computational Optimization and Applications 78 ( 2021), 377–410.
Eric R. Keiter, Laura P. Swiler, and Ian Z. Wilcox. 2018. Gradient-enhanced polynomial chaos methods for circuit simulation. In Scientific Computing in Electrical Engineering. Ulrich Langer, Wolfgang Amrhein, and Walter Zulehner (Eds.), Springer International Publishing, Cham, 55–68. DOI: 10.1007/978-3-319-75538-0_6
Brian Kelley and Sivasankaran Rajamanickam. 2022. Parallel, portable algorithms for distance-2 maximal independent set and graph coarsening. In 2022 IEEE International Parallel and Distributed Processing Symposium (IPDPS). IEEE, IEEE Computer Society, Los Alamitos, CA, 280–290.
Sarah L. Kieweg, Jaideep Ray, V. G. Weirs, Brian Carnes, Derek Dinzl, Brian Freno, Micah Howard, Eric Phipps, William Rider, and Thomas Smith. 2019. Validation assessment of hypersonic double-cone flow simulations using uncertainty quantification, sensitivity analysis, and validation metrics. In AIAA Scitech 2019 Forum. DOI: 10.2514/6.2019-2278
Kyungjoo Kim, Timothy B. Costa, Mehmet Deveci, Andrew M. Bradley, Simon D. Hammond, Murat E. Guney, Sarah Knepper, Shane Story, and Sivasankaran Rajamanickam. 2017. Designing vector-friendly compact BLAS and LAPACK kernels. In International Conference for High Performance Computing, Networking, Storage and Analysis. ACM, New York, NY, USA, 1–12.
K. Kim, H. C. Edwards, and S. Rajamanickam. 2018. Tacho: Memory-scalable task parallel sparse Cholesky factorization. In 2018 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW). DOI: 10.1109/IPDPSW.2018.00094
Drew P. Kouri. 2022. A matrix-free trust-region newton algorithm for convex-constrained optimization. Optimization Letters 16, 3 (2022), 983–997. DOI: 10.1007/s11590-021-01794-1
D. P. Kouri, M. Heinkenschloss, D. Ridzal, and B. G. van Bloemen Waanders. 2013. A trust-region algorithm with adaptive stochastic collocation for PDE optimization under uncertainty. SIAM Journal on Scientific Computing 35, 4 (2013), A1847–A1879.
D. P. Kouri, M. Heinkenschloss, D. Ridzal, and B. G. van Bloemen Waanders. 2014. Inexact objective function evaluations in a trust-region algorithm for PDE-constrained optimization under uncertainty. SIAM Journal on Scientific Computing 36, 6 (2014), A3011–A3029.
Drew P. Kouri and Denis Ridzal. 2018. Inexact Trust-Region Methods for PDE-Constrained Optimization. Springer, New York, NY, 83–121. DOI: 10.1007/978-1-4939-8636-1_3
Drew P. Kouri and Eric A. Shields. 2014. Efficient multiframe super-resolution for imagery with lateral shifts. Applied Optics 53, 24, (Aug. 2014), F1–F9. DOI: 10.1364/AO.53.0000F1
Drew P. Kouri and Thomas M. Surowiec. 2022. A primal–dual algorithm for risk minimization. Mathematical Programming 193, 1 (2022), 337–363.
Paul Kuberry, Pavel Bochev, Jake Koester, and Nathaniel Trask. 2025. A discontinuous piecewise polynomial generalized moving least squares scheme for robust finite element analysis on arbitrary grids. Engineering with Computers 41, 3 (2025), 1435–1554. DOI: 10.1007/s00366-024-02036-5
Kim Liegeois, Romain Boman, Eric T. Phipps, Tobias A. Wiesner, and Maarten Arnst. 2020. GMRES with embedded ensemble propagation for the efficient solution of parametric linear systems in uncertainty quantification of computational models. Computer Methods in Applied Mechanics and Engineering 369 ( 2020), 113188.
Kim Liegeois, Sivasankaran Rajamanickam, and Luc Berger-Vergiat. 2023. Performance portable batched sparse linear solvers. IEEE Transactions on Parallel and Distributed Systems 34, 5 (2023), 1524–1535.
Paul T. Lin, John N. Shadid, Jonathan J. Hu, Roger P. Pawlowski, and Eric C. Cyr. 2017. Performance of fully-coupled algebraic multigrid preconditioners for large-scale VMS resistive MHD. Journal of Computational and Applied Mathematics 344 ( 2017), 782–793.
K. Long, Paul T. Boggs, and Bart G. van Bloemen Waanders. 2012. Sundance: High-level software for PDE-constrained optimization. Scientific Programming 20, 3 (2012), 293–310. DOI: 10.3233/SPR-2012-0341
V. S. Mahadevan, J. E. Guerra, X. Jiao, P. Kuberry, Y. Li, P. Ullrich, D. Marsico, R. Jacob, P. Bochev, and P. Jones. 2022. Metrics for Intercomparison of Remapping Algorithms (MIRA) protocol applied to Earth system models. Geoscientific Model Development 15, 17 (2022), 6601–6635. DOI: 10.5194/gmd-15-6601-2022
Matthias Mayr, Luc Berger-Vergiat, Peter Ohm, and Raymond S. Tuminaro. 2022. Non-invasive multigrid for semi-structured grids. SIAM Journal on Scientific Computing 44, 4 (2022), A2734–A2764. DOI: 10.1137/20M1375413
Matthias Mayr, Christian A. Glusa, Graham B. Harper, Jonathan J. Hu, Andrey Prokopenko, and Tobias A. Wiesner. 2025. The MueLu Tutorial. Retrieved from https://muelu.github.io/
S. T. Miller, E. C. Cyr, J. N. Shadid, R. M. J. Kramer, E. G. Phillips, S. Conde, and R. P. Pawlowski. 2019. IMEX and exact sequence discretization of the multi-fluid plasma model. Journal of Computational Physics 397 ( 2019), 108806. DOI: 10.1016/j.jcp.2019.05.052
Davoud Mirzaei, Robert Schaback, and Mehdi Dehghan. 2012. On generalized moving least squares and diffuse derivatives. IMA Journal of Numerical Analysis 32, 3 (2012), 983–1000.
Karla Morris, Damian W. I. Rouson, M. Nicole Lemaster, and Salvatore Filippone. 2012. Exploring capabilities within ForTrilinos by solving the 3D burgers equation. Scientific Programming 20, 3 (2012), 275–292. DOI: 10.3233/SPR-2012-0353
Lawrence C. Musson, Gary L. Hennigan, Xujiao Gao, Richard Humphries, Mihai Negoita, and Andy Huang. 2020. Charon Users Manual: v. 2.1 (revision1). Technical Report SAND2020-5266. Sandia National Laboratories.
Lawrence C. Musson, Roger P. Pawlowski, Andrew G. Salinger, Timothy J. Madden, and Kevin B. Hewett. 2009. Multiphase reacting flow modeling of singlet oxygen generators for chemical oxygen iodine lasers. In XVII International Symposium on Gas Flow, Chemical Lasers, and High-Power Lasers. Rui Vilar, Olinda Conde, Marta Fajardo, Luís O. Silva, Margarida Pires, and Andrei Utkin (Eds.), Vol. 7131, International Society for Optics and Photonics, SPIE, 148–155. DOI: 10.1117/12.816415
Patrick K. Notz, Roger P. Pawlowski, and James C. Sutherland. 2012. Graph-based software design for managing complexity and enabling concurrency in multiphysics PDE software. ACM Transactions on Mathematical Software 39, 1, Article 1 (Nov. 2012), 21 pages. DOI: 10.1145/2382585.2382586
Peter Ochs, Yunjin Chen, Thomas Brox, and Thomas Pock. 2014. iPiano: Inertial proximal algorithm for nonconvex optimization. SIAM Journal on Imaging Sciences 7, 2 (2014), 1388–1419. DOI: 10.1137/130942954
Peter Ohm, Tobias A. Wiesner, Eric C. Cyr, Jonathan J. Hu, John N. Shadid, and Raymond S. Tuminaro. 2022. A monolithic algebraic multigrid framework for multiphysics applications with examples from resistive MHD. ETNA—Electronic Transactions on Numerical Analysis 55 ( 2022), 365–390. DOI: 10.1553/etna_vol55s365
Ron A. Oldfield, Gregory D. Sjaardema, Gerald F. Lofstead, II, and Todd Kordenbrock. 2012. Trilinos I/O support (Trios). Scientific Programming 20, 2 (2012), 181–196. DOI: 10.3233/SPR-2012-0345
Anthony D. Padula, Shannon D. Scott, and William W. Symes. 2009. A software framework for abstract expression of coordinate-free linear algebra and optimization algorithms. ACM Transactions on Mathematical Software 36, 2 (2009), 1–36. DOI: 10.1145/1499096.1499097
Albert E. Parker and Colin Fox. 2012. Sampling Gaussian distributions in Krylov spaces with conjugate gradients. SIAM Journal on Scientific Computing 34, 3 (2012), B312–B334.
Roger P. Pawlowski, Eric T. Phipps, and Andrew G. Salinger. 2012. Automating embedded analysis capabilities and managing software complexity in multiphysics simulation, part I: Template-based generic programming. Scientific Programming 20, 2 (2012), 197–219.
Roger P. Pawlowski, Eric T. Phipps, Andrew G. Salinger, Steven J. Owen, Christopher M. Siefert, and Matthew L. Staten. 2012. Automating embedded analysis capabilities and managing software complexity in multiphysics simulation, part II: Application to partial differential equations. Scientific Programming 20, 3 (2012), 327–345.
Roger P. Pawlowski, Andrew G. Salinger, Louis R. Romero, and John N. Shadid. 2001. Computational design and analysis of MOVPE reactors. Journal de Physique IV France 11, PR3 (2001), Pr3-197–Pr3-204. DOI: 10.1051/jp4:2001325
R. P. Pawlowski, A. G. Salinger, J. N. Shadid, and T. J. Mountziaris. 2006. Bifurcation and stability analysis of laminar isothermal counterflowing jets. Journal of Fluid Mechanics 551 ( 2006), 117–139. DOI: 10.1017/S0022112005008396
Roger P. Pawlowski, John N. Shadid, Joseph P. Simonis, and Homer F. Walker. 2006. Globalization techniques for Newton–Krylov methods and applications to the fully coupled solution of the Navier–Stokes equations. SIAM Review 48, 4 (2006), 700–721. DOI: 10.1137/S0036144504443511
Roger P. Pawlowski, Joseph P. Simonis, Homer F. Walker, and John N. Shadid. 2008. Inexact newton dogleg methods. SIAM Journal on Numerical Analysis 46, 4 (2008), 2112–2132. DOI: 10.1137/050632166
Mauro Perego. 2022. Large-Scale PDE-Constrained Optimization for Ice Sheet Model Initialization. SIAM News. Retrieved from https://sinews.siam.org/Details-Page/large-scale-pde-constrained-optimization-for-ice-sheet-model-initialization
Eric Phipps, H. Carter Edwards, Jonathan Hu, and Jakob T. Ostien. 2014. Exploring emerging manycore architectures for uncertainty quantification through embedded stochastic Galerkin methods. International Journal of Computer Mathematics 91, 4 (2014), 707–729.
Eric Phipps and Roger Pawlowski. 2012. Efficient expression templates for operator overloading-based automatic differentiation. In Recent Advances in Algorithmic Differentiation. Springer, Berlin, 309–319.
Eric Phipps, Roger Pawlowski, and Christian Trott. 2022. Automatic differentiation of C++ codes on emerging manycore architectures with Sacado. ACM Transactions on Mathematical Software 48, 4 (2022), 1–29.
Eric T. Phipps, Roscoe A. Bartlett, David M. Gay, and Robert J. Hoekstra. 2008. Large-scale transient sensitivity analysis of a radiation-damaged bipolar junction transistor via automatic differentiation. Advances in Automatic Differentiation 64 (2008), 351–362.
E. Phipps, M. D'Elia, H. C. Edwards, M. Hoemmen, J. Hu, and S. Rajamanickam. 2017. Embedded ensemble propagation for improving performance, portability, and scalability of uncertainty quantification on emerging computational architectures. SIAM Journal on Scientific Computing 39, 2 (2017), C162–C193.
E. T. Phipps and D. M. Gay. 2011. Sacado Automatic Differentiation Package. Retrieved from http://trilinos.sandia.gov/packages/sacado/
Eric T. Phipps and Andrew G. Salinger. 2016. Embedded Uncertainty Quantification Methods via Stokhos. Springer International Publishing, Cham, 1–43. DOI: 10.1007/978-3-319-11259-6_55-1
Sivasankaran Rajamanickam, Seher Acer, Luc Berger-Vergiat, Vinh Dang, Nathan Ellingwood, Evan Harvey, Brian Kelley, Christian R. Trott, Jeremiah Wilke, and Ichitaro Yamazaki. 2021. Kokkos kernels: Performance portable sparse/dense linear algebra and graph kernels. arXiv:2103.11991. Retrieved from https://arxiv.org/abs/2103.11991
R. T. Rockafellar and Roger J.-B. Wets. 1991. Scenarios and policy aggregation in optimization under uncertainty. Mathematics of Operations Research 16, 1 (1991), 119–147.
Youcef Saad. 1993. A flexible inner-outer preconditioned GMRES algorithm. SIAM Journal on Scientific Computing 14, 2 (1993), 461–469. DOI: 10.1137/0914028
Marzio G. Sala and Ray S. Tuminaro. 2008. A new Petrov–Galerkin smoothed aggregation preconditioner for nonsymmetric linear systems. SIAM Journal on Scientific Computing 31, 1 (2008), 143–166. DOI: 10.1137/060659545
A. G. Salinger, E. A. Burroughs, R. P. Pawlowski, E. T. Phipps, and L. A. Romero. 2005. Bifurcation tracking algorithms and software for large scale applications. International Journal of Bifurcation and Chaos 15, 3 (2005), 1015–1032.
Andrew Salinger and Eric T. Phipps. 2010. Piro v. 1.0, Version 00. Retrieved from https://www.osti.gov/biblio/1231283
Andrew G. Salinger, Roscoe A. Bartlett, Andrew M. Bradley, Qiushi Chen, Irina P. Demeshko, Xujiao Gao, Glen A. Hansen, Alejandro Mota, Richard P. Muller, Erik Nielsen, et al. 2016. Albany: Using component-based design to develop a flexible, generic multiphysics analysis code. International Journal for Multiscale Computational Engineering 14, 4 (2016), 415–438.
Andrew G. Salinger, Richard B. Lehoucq, Roger P. Pawlowski, and John N. Shadid. 2002. Computational bifurcation and stability studies of the 8:1 thermal cavity problem. International Journal for Numerical Methods in Fluids 40, 8 (2002), 1059–1073. DOI: 10.1002/fld.392
Helga Schramm and Jochem Zowe. 1992. A version of the bundle idea for minimizing a nonsmooth function: Conceptual idea, convergence analysis, numerical results. SIAM Journal on Optimization 2, 1 (1992), 121–152. DOI: 10.1137/0802008
J. N. Shadid, A. G. Salinger, R. P. Pawlowski, P. T. Lin, G. L. Hennigan, R. S. Tuminaro, and R. B. Lehoucq. 2006. Large-scale stabilized FE computational analysis of nonlinear steady-state transport/reaction systems. Computer Methods in Applied Mechanics and Engineering 195, 13 (2006), 1846–1871. DOI: 10.1016/j.cma.2005.05.047
J. N. Shadid, R. P. Pawlowski, E. C. Cyr, R. S. Tuminaro, L. Chacon, and P. D. Weber. 2016. Scalable implicit incompressible resistive MHD with stabilized FE and fully-coupled Newton-Krylov-AMG. Computer Methods in Applied Mechanics and Engineering 304 ( 2016), 1–25. DOI: 10.1016/j.cma.2016.01.019
J. N. Shadid, T. M. Smith, E. C. Cyr, T. M. Wildey, and R. P. Pawlowski. 2016. Stabilized FE simulation of prototype thermal-hydraulics problems with integrated adjoint-based capabilities. Journal of Computational Physics 321 ( 2016), 321–341. DOI: 10.1016/j.jcp.2016.04.062
Alexander Shapiro, Darinka Dentcheva, and Andrzej Ruszczynski. 2021. Lectures on Stochastic Programming: Modeling and Theory. SIAM.
David Sondak, Thomas M. Smith, Roger P. Pawlowski, Sidafa Conde, and John N. Shadid. 2021. High Rayleigh number variational multiscale large eddy simulations of Rayleigh-Bénard convection. Mechanics Research Communications 112 ( 2021), 103614. DOI: 10.1016/j.mechrescom.2020.103614
William F. Spotz. 2012. PyTrilinos: Recent advances in the python interface to Trilinos. Scientific Programming 20, 3 (2012), 311–325. DOI: 10.3233/SPR-2012-0346
S. J. Thomas, S. Ananthan, S. Yellapantula, Jonathan J. Hu, M. Lawson, and Michael A. Sprague. 2019. A comparison of classical and aggregation-based algebraic multigrid preconditioners for high-fidelity simulations of wind turbine incompressible flows. SIAM Journal on Scientific Computing 41, 5 (2019), S196–S219.
H. K. Thornquist and S. Rajamanickam. 2014. A hybrid approach for parallel transistor-level full-chip circuit simulation. In International Conference on High Performance Computing for Computational Science. Springer, Cham, 102–111.
Christian Trott, Luc Berger-Vergiat, David Poliakoff, Sivasankaran Rajamanickam, Damien Lebrun-Grandie, Jonathan Madsen, Nader Al Awar, Milos Gligoric, Galen Shipman, and Geoff Womeldorff. 2021. The Kokkos ecosystem: Comprehensive performance portability for high performance computing. Computing in Science & Engineering 23, 5 (2021), 10–18.
Christian R. Trott, Damien Lebrun-Grandié, Daniel Arndt, Jan Ciesko, Vinh Dang, Nathan Ellingwood, Rahulkumar Gayatri, Evan Harvey, Daisy S. Hollman, Dan Ibanez, et al. 2022. Kokkos 3: Programming model extensions for the exascale era. IEEE Transactions on Parallel and Distributed Systems 33, 4 (2022), 805–817. DOI: 10.1109/TPDS.2021.3097283
Raymond S. Tuminaro, Mauro Perego, Irina Tezaur, Andrew G. Salinger, and S. Price. 2016. A matrix dependent/algebraic multigrid approach for extruded meshes with applications to ice sheet modeling. SIAM Journal on Scientific Computing 38, 5 (2016), C504–C532. DOI: 10.1137/15M1040839
S. P. Vanka. 1986. Block-implicit multigrid solution of Navier-Stokes equations in primitive variables. Journal of Computational Physics 65, 1 (1986), 138–158.
Petr Vaněk, Jan Mandel, and Marian Brezina. 1996. Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems. Computing 56 ( 1996), 179–196.
Homer F. Walker and Peng Ni. 2011. Anderson acceleration for fixed-point iterations. SIAM Journal on Numerical Analysis 49, 4 (2011), 1715–1735. DOI: 10.1137/10078356X
Holger Wendland. 2004. Data Approximation, Vol. 17. Cambridge University Press.
Tobias A. Wiesner, Matthias Mayr, Alexander Popp, Michael W. Gee, and Wolfgang A. Wall. 2021. Algebraic multigrid methods for saddle point systems arising from mortar contact formulations. International Journal for Numerical Methods in Engineering 122, 15 (2021), 3749–3779. DOI: 10.1002/nme.6680
Michael M. Wolf, Mehmet Deveci, Jonathan W. Berry, Simon D. Hammond, and Sivasankaran Rajamanickam. 2017. Fast linear algebra-based triangle counting with KokkosKernels. In 2017 IEEE High Performance Extreme Computing Conference (HPEC). IEEE, Los Alamitos, CA, USA, 1–7.
Pavan Yalamanchili, Umar Arshad, Zakiuddin Mohammed, Pradeep Garigipati, Peter Entschev, Brian Kloppenborg, James Malcolm, and John Melonakos. 2015. ArrayFire—A high performance software library for parallel computing with an easy-to-use API. Retrieved from https://github.com/arrayfire/arrayfire
Ichitaro Yamazaki, Alexander Heinlein, and Sivasankaran Rajamanickam. 2023. An experimental study of two-level Schwarz domain-decomposition preconditioners on GPUs. IEEE Computer Society, 680–689. DOI: 10.1109/IPDPS54959.2023.00073