This article presents a parallel, effective, and feature-complete recursive SPIKE algorithm that achieves near feature-parity with the standard linear algebra package banded linear system solver. First, we present a flexible parallel implementation of the recursive SPIKE scheme that aims at removing its original limitation that the number of cores/processors be restricted to powers of two. A new transpose solve option for SPIKE is then developed to satisfy a standard requirement of most numerical solver libraries. Finally, a pivoting recursive SPIKE strategy is presented as an alternative to the non-pivoting scheme to improve numerical stability. All these new enhancements lead to the release of a new black-box feature-complete SPIKE-OpenMP package that significantly improves upon the performance and scalability obtained with other state-of-the-art banded solvers.

The FEAST algorithm and eigensolver for interior eigenvalue problems naturally possesses three distinct levels of parallelism. The solver is then suited to exploit modern computer architectures containing many interconnected processors. This paper highlights a recent development within the software package that allows the dominant computational task, solving a set of complex linear systems, to be performed with a distributed memory solver. The software, written with a reverse-communication-interface, can now be interfaced with any generic MPI linear-system solver using a customized data distribution for the eigenvector solutions. This work utilizes two common “black-box” distributed memory linear-systems solvers (Cluster-MKL-Pardiso and MUMPS), as well as our own application-specific domain-decomposition MPI solver, for a collection of 3-dimensional finite-element systems. We discuss and analyze how parallel resources can be placed at all three levels simultaneously in order to achieve good scalability and optimal use of the computing platform.