Holistic Performance Engineering for Sparse Iterative Solvers

Abstract

In many applications, sparse (linear and/or eigenvalue) solvers take up a large fraction of the overall runtime. We believe that the increasingly complex hardware of today's and future HPC systems has lead to a gap in the understanding of the performance achieved by actual applications, many of which are still using a monolithic `MPI only' approach despite the heterogeneous nature of the hardware. We have developed a new sparse solver library PHIST (https://bitbucket.org/essex/phist/) that defines a simple "kernel interface" layer inspired by MPI. Algorithms implemented in PHIST are portable in terms of software and performance as they only call building blocks of linear algebra via this interface. We have introduced simple performance models for these basic building blocks at the interface level, so that regardless of the backend providing the implementation, an overview of the optimization potential on the kernel level can be obtained, and performance pitfalls in the application (e.g. strided memory accesses) may be revealed. Available backends for PHIST include established libraries such as Trilinos/Epetra or PETSc, as well as more recent "MPI+X" approaches as implemented in Trilinos/Tpetra or our own kernel library GHOST (https://bitbucket.org/essex/ghost).