Many simulation and data analysis codes need to solve sparse systems of equations. The high-fidelity simulations being solved by exascale application teams involve large-scale multiphysics and multiscale modeling problems that generate highly ill-conditioned and indefinite systems, for which iterative methods struggle. The STRUMPACK/SuperLU project is delivering robust and scalable factorization-based algorithms that are indispensable building blocks for solving these numerically challenging problems.
Scalable factorization-based methods are important components in solvers for ill-conditioned and indefinite systems of equations that arise in many exascale applications. The STRUMPACK/SuperLU project is producing robust and scalable factorization-based algorithms that can be used as direct solvers or preconditioners for linear systems of equations.
The team is delivering factorization-based sparse solvers that encompass two widely used algorithm variants: the supernodal SuperLU library and the multifrontal STRUMPACK library. The team is also adding scalable preconditioning functionality to the STRUMPACK library via hierarchical matrix algebra. Both libraries are applicable to a large variety of application domains. These scalable libraries are being enhanced to ensure that they will be performant on pre-exascale and exascale architectures.
Both SuperLU and STRUMPACK can be used as stand-alone solvers. More importantly, for ECP applications, critical subsolvers are being used in the higher level solver libraries, such as coarse grid solvers in a multigrid solver, subdomain solvers in a domain decomposition solver, block diagonal preconditioners in a Krylov iterative solver, or general approximate factorization preconditioners for an iterative solver.