Scalable Linear Solvers

The Scalable Linear Solvers project is developing scalable algorithms and software for the solution of large, sparse linear systems of equations on massively parallel computers. Such algorithms are crucial for achieving overall scalability in many LLNL and ASC simulation codes. The first major component of the project is multilevel methods research, including geometric and algebraic multigrid, domain decomposition, hierarchical basis, and multilevel ILU methods. The second major component is the development of "hypre", a parallel library of high-performance preconditioners to be used as both a stand-alone package, as well as a plug-in package for other solver libraries.

We are conducting algorithms research in three main areas: geometric multigrid methods for structured mesh problems, algebraic multigrid methods for unstructured mesh problems, and sparse approximate inverse and incomplete factorization methods as more general-purpose matrix solvers for structured, unstructured, and nonsymmetric problems.

We are investigating mixed programming models such as MPI/Pthreads and MPI/OpenMP to better exploit ASC machine resources. We are also researching various library and language interoperability issues and working on object-oriented design issues as part of the Equation Solver Interface (ESI) forum. Finally, "hypre" is driving research on software quality control and software support issues.