# Implementation of Numerical Integration to High-Order Elements on the GPUs

### Abstract

This article presents ways to implement a resource-consuming algorithm on hardware with a limited amount of memory, which is the GPU. Numerical integration for higher-order finite element approximation was chosen as an example algorithm. To perform computational tests, we use a non-linear geometric element and solve the convection-diffusion-reaction problem. For calculations, a Tesla K20m graphics card based on Kepler architecture and Radeon r9 280X based on Tahiti XT architecture were used. The results of computational experiments were compared with the theoretical performance of both GPUs, which allowed an assessment of actual performance. Our research gives suggestions for choosing the optimal design of algorithms as well as the right hardware for such a resource-demanding task.

### Keywords

GPU, Numerical Integration, Finite Elemet Method, OpenCL, CUDA,### References

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**Computer Assisted Methods in Engineering and Science**, [S.l.], v. 27, n. 1, p. 3-26, apr. 2020. ISSN 2956-5839. Available at: <https://cames.ippt.pan.pl/index.php/cames/article/view/264>. Date accessed: 06 june 2023. doi: http://dx.doi.org/10.24423/cames.264.