FASTMath SciDAC Institute
Research Team

The FASTMath team brings together preeminent scientists in a broad range of applied mathematics areas. The FASTMath team has a proven track record of developing new mathematical technologies and algorithms, tackling difficult algorithmic and implementation issues as computer architectures undergo a fundamental shift, and engaging multiple application domains to enable new scientific discovery. 

More than 50 mathematicians from five national laboratories and five universities comprise our team.

Argonne National Laboratory

Our FASTMath work focuses on iterative solvers, numerical optimization, and adjoint and forward sensitivities. We are investigating issues in data layout and programming models to achieve efficient and scalable performance on emerging extreme-scale architectures. We are developing numerical methods for solving dynamic optimization problems with partial differential equation constraints that may include nontrivial design and state constraints, integer variables, and multiple objectives. The methods span derivative-free and derivate-required algorithms. We are also developing advanced adjoint and forward sensitivitity capabilities that arise in dynamic optimization problems and data assimilation.


Barry Smith
Stefan Wild
Hong Zhang
Sven Leyffer
Lois Curfman McInnes
Todd Munson

Mathematics and Computer Science Division, Argonne National Laboratory, 9700 South Cass Avenue, Building 240, Argonne, IL 60439


Lawrence Berkeley National Laboratory

We are developing scalable mathematical algorithms and software tools for current and future high-performance computing architectures. Our areas of expertise include finite volume methods in structured grid AMR frameworks, unstructured mesh discretization technologies for particle methods, high-order temporal discretizations for structured mesh calculations, highly optimized solvers for sparse systems of linear equations, eigensolvers, and optimization techniques for predicting parameter sensitivities in applications. Software developed by FASTMath team members at Berkeley Lab comprises the framework and/or solver technology for application codes in accelerator modeling, astrophysics, cosmology, catalysis, materials science, and ice sheet modeling. Software developed by Berkeley Lab FASTMath team members is publicly available by download through the individual web sites. Visit the LBNL FASTMath site for more information.


Ann Almgren
Mark Adams
Pieter Ghysels
Robert Saye
Chao Yang
Juliane Mueller
Michael Minion
Sherry Li
Mathias Jacquelin
Daniel Martin
Phil Colella
Peter McCorquodale
Osni Marques
Esmond G. Ng

Lawrence Berkeley National Laboratory, One Cyclotron Road, Mail Stop 50A3111, Berkeley, CA 94720


Lawrence Livermore National Laboratory

LLNL team members are involved in several aspects of the FASTMath proposal. In particular we are responsible for research and development of scalable algorithms for unstructured grids using MFEM, multigrid iterative solvers in hypre, time integration and nonlinear solvers in SUNDIALS, and parallel in time algorithms in xBraid. Our efforts will address parallel conforming and non-conforming mesh adaptation for curved domains that can evolve in time, including curved mesh entities for high-order methods. Our efforts will address support for goal-oriented error estimation through the development of generalized methods to integrate adjoint methods. Error estimation methods on non-conforming meshes will be developed in MFEM. We will pursue several efforts to develop multigrid methods that are highly scalable and provide robust solutions for various applications, including the design of high-performance implementations of {\it multilevel algorithms for strongly coupled multi-physics systems. We will implement a complex-valued algebraic multigrid solver in hypre. Finally, we will investigate various ways to increase robustness of current multigrid solvers in hypre, e.g., more sophisticated smoothers, such as ILU smoothers, to allow for the solution of notoriously difficult linear systems that arise in some applications. We will develop a new software framework for additive — integrators within the SUNDIALS suite of advanced time integrators and nonlinear solvers. We will make the MGRIT parallel-in-time integration methodology available to SUNDIALS users through incorporation of the xBraid package into a time-parallel version of the ARKode package within SUNDIALS. We will improve robustness of the CVODE and ARKode integration packages in SUNDIALS. Finally, we provide overall leadership for the project and support for team collaboration through a web-based development site.    


Rob Falgout
Ruipeng Li
Veselin Dobrev
Jacob Schroder
John Loffeld
Carol Woodward
David Gardner
Ulrike Yang
Tzanio Kolev
Lori Diachin

Lawrence Livermore National Laboratory, Box 808, L-561, Livermore, CA 94551-0808


Massachusetts Institute of Technology

The MIT FASTMath effort focuses on computational methods for parameter inference and inverse problems in the Bayesian setting. These methods enable data-driven calibration and uncertainty quantification in a wide range of simulation models. Key algorithmic efforts include (i) error-controlled dimension reduction strategies for high-dimensional inference problems, and (ii) the online construction/refinement of inference-focused surrogate models via local and global function approximation strategies. These algorithms will be embedded in Markov chain Monte Carlo methods suitable for large-scale problems.

For more information:


Youssef Marzouk

Department of Aeronautics and Astronautics, Room 37-451, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139