Matrix-free finite-element operator application on graphics processing units

Abstract

In this paper, methods for efficient utilization of modern accelerator-based hardware for performing high-order finite-element computations are studied.We have implemented several versions of a matrixfree finite-element stiffness operator targeting graphics processors. Two different techniques for handling the issue of conflicting updates are investigated; one approach based on CUDA atomics, and a more advanced approach using mesh coloring. These are contrasted to a number of matrix-free CPU-based implementations. A comparison to standard matrix-based implementations for CPU and GPU is also made. The performance of the different approaches are evaluated through a series of benchmarks corresponding to a Poisson model problem. Depending on dimensionality and polynomial order, the best GPU-based implementations performed between four and ten times faster than the fastest CPU-based implementation.