Efficient Heuristic Adaptive Quadrature on GPUs: Design and Evaluation

Numerical integration is a common sub-problem in many applications. It can be solved easily in CPU-based applications using adaptive quadrature such as the adaptive Simpson's rule. These algorithms rely, however, on error estimation yielding a significant computational overhead. In addition, they require recursive function evaluations, which are not well suited for parallel computation on graphics processing units (GPUs) due to warp divergence issues. In this paper, we introduce heuristic forward quadrature as an alternative that is not only more efficient than traditional methods, but also better suited for accelerated massively-parallel calculation on GPUs. Additionally, we will give an error estimate for our method and demonstrate performance results for 1D and 2D integral applications which show that the algorithm leverages quadrature for the efficient implementation on GPUs.