The changing landscape of both scientific application needs and high-performance computing systems requires continued innovation in mathematical algorithms and software for robust, efficient, and scalable solvers. Based on the needs of the former and the properties (and constraints) of the latter, we will extend PETSc's composable, hierarchical, nested solvers---that is, solvers composed of multiple levels of nested algorithms and data models---to exploit architectural features and problem-specific structure. We holistically address memory hierarchy, vectorization, heterogeneous computing, and new scientific demands by combining advances across (1) solvers and integrators, (2) models and discretizations, and (3) mesh and data management through three subprojects.
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DMNetwork: composable multiphysics PDE-based network simulations: robust, scalable simulation framework for large-scale network applications, such as power-grid and water networks;
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SITAR: solver-integrated tree-based adaptive refinement: high-efficiency meta-multigrid solvers with adaptivity, as motivated by modeling in fusion, geodynamics, and nuclear reactors; and
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Outer-loop computations: integrated solver and data management capabilities needed for work toward predictive science, including construction of auxiliary heterogeneous subsystems, as needed by numerical optimization and synthesis of data-intensive and simulation-intensive components
These scalable solvers will benefit numerous applications and thus will have a powerful impact on a broad range of important Office of Science and other DOE work.
