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.
Nearly 50 mathematicians from four national laboratories and seven universities comprise our team.
Argonne National Laboratory
Our FASTMath work focuses on complementary aspects of scalable iterative solvers and meshing for complex geometry. We are investigating issues in data layout and programming models to achieve efficient and scalable performance on emerging extreme-scale architectures. We are also addressing interoperability among FASTMath technologies, including interfaces between solvers and both structured and unstructured meshing, particle to mesh coupling, and mesh to mesh coupling. Lastly, we are focusing on the development of numerical methods for solving differential variational inequalities in the nonlinear solvers of PETSc—specifically, scalable active-set methods for both compact and extended systems that include repartitioning of the active sets and that leverage the multigrid component of FASTMath.
Lawrence Berkeley National Laboratory
We are developing scalable mathematical algorithms and software tools for high-performance computing architectures. Our research areas include finite volume methods and particle/mesh methods in structured grid AMR frameworks, high-order discretization methods, highly optimized linear and nonlinear solvers, and eigensolvers. Software developed by our FASTMath team members comprises the framework and/or solver technology for application codes in accelerator modeling, astrophysics, climate, combustion, cosmology, material science and porous media and is publicly available by download through the project web sites. Visit the LBNL FASTMath site for more information.
Lawrence Livermore National Laboratory
LLNL team members are involved in nearly all aspects of the FASTMath proposal. In particular we are responsible for research and development of scalable algorithms for mapped multiblock algorithms using Chombo, mesh quality improvement in Mesquite, multigrid solvers in hypre, and nonlinear solvers in SUNDIALS. In all cases, we are striving to minimize communication and data movement costs and develop hierarchical parallelism strategies using mixed programming models for many core architecture. We are implementing a block-structured AMR multigrid solver that takes advantage of structure, refining the semi-structured interface in hypre, and implementing support for updating matrices, vectors, and solvers in AMR settings. We are working with FASTMath team members to extend the iField interface to support structured meshes and particle methods. We are also helping to define and support the essential practices for FASTMath-compliant software products and develop integrated tests. Finally, we provide overall leadership for the project and support for team collaboration through a web-based development site.
Rensselaer Polytechnic Institute and University of Colorado Boulder
We are focused on the development of all aspects of exascale unstructured mesh methods. Efforts include the development of highly scalable finite element based solvers, parallel mesh infrastructures, general anisotropic mesh adaptation procedures for general 3D domains including curved high order mesh entities, unstructured mesh adjacency based partitioning tools, interactions with general geometry representations, and a unstructured mesh fields infrastructure.