BLAST Motivated Small Dense Linear Algebra Library Comparison
Authors: Pate Motter (University of Colorado Boulder), Ian Karlin (Lawrence Livermore National Laboratory), Christopher Earl (Lawrence Livermore National Laboratory)
Abstract: Future computing architectures will be more memory bandwidth bound than current machines. Higher-order algorithms are more compute intense and can take advantage of the extra compute capabilities of future machines to produce higher quality answers. In this poster we focus on BLAST, an arbitrary order arbitrary Lagrangian-Eulerian (ALE) finite element code. Typical of finite element codes, BLAST requires both global sparse and local dense matrix solves. The dense matrix solves and sparse matrix assembly perform numerous small, dense matrix calculations and consume most of its runtime. Many libraries focus on optimizing small linear algebra operations. We created a benchmark suite that mimics BLAST’s most computationally intensive portions, currently implemented using MFEM. We use this suite to explore the performance of these libraries. For our benchmarks Armadillo, Blaze, and a template-based version of MFEM all produce promising results. Eigen’s feature set made it promising; however, its performance was not competitive.
Two-page extended abstract: pdf