A survey of sparse matrix-vector multiplication performance on large matrices

One of the main sources of sparse matrices is the discretization of partial differential equations that govern continuumphysics phenomena such as fluid flow and transport, phase separation, mechanical deformation, electromagnetic wave propagation, and others. Recent advances in high-performance computing area have been enabling researchers to tackle increasingly larger problems leading to sparse linear systems with hundreds of millions to a few tens of billions of unknowns, e.g., [5, 6]. Iterative linear solvers are popular in large-scale computing as they consume less memory than direct solvers. Contrary to direct linear solvers, iterative solvers approach the solution gradually requiring the computation of sparse matrixvector (SpMV) products. The evaluation of SpMV products can emerge as a bottleneck for computational performance within the context of the simulation of large problems. In this work, we focus on a linear system arising from the discretization of the Cahn–Hilliard equation, which is a fourth order nonlinear parabolic partial differential equation that governs the separation of a two-component mixture into phases [3]. The underlying spatial discretization is performed using the discontinuous Galerkin method (e.g. [10]) and Newton’s method. A number of parallel algorithms and strategies have been evaluated in this work to accelerate the evaluation of SpMV products.