Sparse Solvers on Extreme-Scale Systems

Abstract. We introduce and develop algorithms for the solution of sparse linear systems providing background and an overview for the other talks in this minisymposium. We also consider some aspects of the topic not considered by the other talks.

For the direct solution of symmetrically structured systems, we express the computation as a DAG and use dense matrix kernels. We consider both multifrontal and supernodal methods and show how numerical pivoting can complicate the exploitation of parallelism providing the background for the second talk in the minisymposium that addresses this issue.

We then discuss in some depth algorithms based on a Markowitz threshold approach for highly unsymmetric systems. The basic algorithms are easy to describe but are very complicated to code efficiently even in serial mode. We show that in spite of the complication they can be designed to enable good levels of parallelism.

We discuss the issues involved in obtaining high parallelism for iterative solvers noting that preconditioners that are effective in the serial case may not work well in parallel. This part of the talk serves as an introduction to the third and fourth talks in the minisymposium. Finally we consider hybrid techniques that combine the best features of direct and iterative methods and give added scope for the exploitation of parallelism

This minisymposium presents research done in NLAFET, a Horizon 2020 FET-HPC project funded by the European Union.