A software framework for Equipping Sparse Solvers for the EXa-scale

Mathematicians and domain scientists who want to implement their algorithms on a supercomputer typically rely on HPC software frameworks to deliver reasonable performance. While it is important to separate the concerns of applications, algorithm and performance to some extent (especially in an increasingly complex hardware landscape), this often leads to a dramatic performance loss in practice because applications may benefit from tailored operations that are not seen as useful in the general setting of a numerical library. A prominent example is the orthogonalization of "tall and skinny" matrices, which leads to memory-bounded performance, so that LAPACK (optimized for compute-bound situations) does not deliver optimal performance. We propose an experimental software stack developed in the ESSEX project that allows on the one hand using existing solutions such as Trilinos, but also leaves the door open for low-level optimized kernels to get the most out of a machine. Using block Krylov and Jacobi-Davidson eigensolvers as an example, we emonstrate how algorithm and kernel development should be combined to achieve good performance. As a second use case, we show how our software stack can be used to parallelize a complete Python software for analyzing nonlinear dynamical systems