## Section: Software

### Parallel solvers for solving linear systems of equations

Participant : Laura Grigori.

In the last several years, there has been significant research effort in the development of fully parallel direct solvers for computing the solution of large unsymmetric sparse linear systems of equations. In this context, we have designed and implemented a parallel symbolic factorization algorithm, which is suitable for general sparse unsymmetric matrices. The symbolic factorization is one of the steps that is sequential and represents a memory bottleneck. The code is intended to be used with very large matrices when because of the memory usage, the sequential algorithm is not suitable. This code is available in the SuperLU_DIST, a widely used software, developed at UC Berkeley and LBNL by Professor James W. Demmel and Dr. Xiaoye S. Li. The algorithm is presented inÂ [101] . The SuperLU_DIST is available at http://crd.lbl.gov/~xiaoye/SuperLU/ .

We continue the development in implementing the numerical factorization phase using the communication avoiding ideas developed this year.