Extending PETSc's Composable, Hierarchical, Nested Solvers

The changing landscape of both scientific application needs (more complex physical models and coupling of diverse models) and high-performance computing systems (many-core node architectures, hybrid combinations of GPU and conventional processors, and high node counts) requires continued innovation in mathematical algorithms for solving sparse linear systems and high-quality, scalable software implementations of these algorithms. To this end, we propose to study composable, hierarchical, nested solvers—that is, solvers composed of multiple levels of nested algorithms and data models to exploit architectural features and/or problem-specific structure. We focus on five complementary subprojects: (1) algorithmic and software infrastructure for nested block methods; (2) scalable solvers for tree-based structured grid adaptive mesh refinement; (3) advanced multigrid methods for multiphysics applications; (4) eigenanalysis of composite linear solvers, allowing one to understand what portions of the solution space are being handled well by the solver and which require additional preconditioning; and (5) software for understanding and analyzing composable, hierarchical, nested solvers in relation to their constituent parts, as well as user composition of such solvers. An essential crosscutting aspect of this work is the development of flexible and extensible software infrastructure to support these hierarchical algorithms. The robust and scalable linear solvers will benefit numerous PDE-based applications, including gyrokinetics, geodynamics, neutron transport, subsurface flow, ice sheet modeling, solid mechanics, and earthquake simulation. Thus, this work will have an immediate and powerful impact on a broad range of important Office of Science and other DOE work.