Optimal Kernel Design for Finite-Element Numerical Integration on GPUs

This article presents the design and optimization of the GPU kernels for numerical integration, as it is applied in the standard form in finite-element codes. The optimization process employs autotuning, with the main emphasis on the placement of variables in the shared memory or registers. OpenCL and the first order finite-element method (FEM) approximation are selected for code design, but the techniques are also applicable to the CUDA programming model and other types of finite-element discretizations (including discontinuous Galerkin and isogeometric). The autotuning optimization is performed for four example graphics processors and the obtained results are discussed.