Highly scalable sparse eigensolvers for large quantum physics problems on heterogeneous computing systems

In the German Research Foundation project ESSEX (Equipping Sparse Solvers for Exascale), we develop scalable sparse eigensolver libraries for large quantum physics problems. Partners in ESSEX are the Universities of Erlangen, Greifswald, Wuppertal, Tokyo and Tsukuba as well as DLR. The project pursues a coherent co-design of all software layers where a holistic performance engineering process guides code development across the classic boundaries of application, numerical method and basic kernel library. Within ESSEX the numerical methods cover widely applicable solvers such as classic Krylov, Jacobi-Davidson or recent FEAST methods and domain specific iterative schemes relevant for the ESSEX quantum physics applications. Using the ESSEX software framework, we present recent work on sparse eigenvalue solvers for heterogeneous computing systems with a focus on the difficult problem of finding interior eigenvalues. In this context, we also discuss the application of the CARP-CG method as a preconditioner for applications such as Graphene simulation