## Factorization Based Sparse Solvers and Preconditioners for Exascale

“Factorization Based Sparse Solvers and Preconditioners for Exascale,” is led by Xiaoye “Sherry” Li, leader of CRD’s Scalable Solvers Group. When researchers try to solve science and engineering problems, they often create systems of linear equations that need to be solved. As science and engineering goals become more ambitious, the number of equations keeps growing, requiring large parallel computers for their solution. Software libraries known as solvers provide mathematical tools that can be applied to problems in areas such as fusion energy, accelerator physics, and analysis of X-ray scattering data.

This project is developing novel techniques for solving large sparse linear systems, and implementing them in two state-of-the-art software packages: SuperLU and STRUMPACK. The resulting mathematical software will enable many multphysics and multiscale simulations with higher resolution and scale, making effective use of the emerging parallel machines. In systems of linear equations that are sparse, where many of the matrix entries are zero and ideally need neither to be stored nor operated on, the strength of SuperLU (which was developed by Li) is that it can automatically determine which matrix entries are zeros and can be ignored, allowing the computer to focus its calculations on the other entries and solve the problem faster.