The Highly Scalable Iterative Solver Library PHIST

As modern supercomputers approach the Exascale, many numerical libraries face scalability issues due to the massive increase in CPU cores compared to memory bandwidth. Sparse matrix algorithms, e.g. iterative linear and eigenvalue solvers, are particularly affected by the relatively slow memory subsystem. In the German Research Foundation (DFG) project ESSEX (Equipping Sparse Solvers for Exascale), we developed the flexible software framework PHIST for implementing iterative methods on HPC systems. PHIST (Pipelined Hybrid Iterative Solver Toolkit) has been developed containing an interface to the existing numerical software framework Trilinos originally. PHIST also includes adapters to basic building block libraries so that high-level algorithm developments can benefit from high-performance kernel implementations, e.g. sparse matrix-vector multiplication kernels. Moreover, PHIST provides systematic and continuous testing of all software components and allows us to develop stable implementations of innovative iterative methods in an evolving hard- and software environment. Using the PHIST framework, we present recent work on sparse eigenvalue solvers, from scalable basic operations to complete algorithms, 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