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2 Computer Assisted Methods in Engineering and Science

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Implementation of numerical integrationto high-order elements on the GPUs

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Krużel F. , Banaś K. , Nytko M.

tom Vol. 27, no. 1

3--26

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 compu- tational 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 archi- tecture 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 sugges- tions for choosing the optimal design of algorithms as well as the right hardware for such a resource-demanding task.

Porting of finite element integration algorithm to Xeon Phi coprocessor-based HPC architectures

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Krużel F. , Banaś K. , Iacomo M.

tom Vol. 30, no. 4

427--459

In the present article, we describe the implementation of the finite element numerical integration algorithm for the Xeon Phi coprocessor. The coprocessor was an extension of the many-core specialized unit for calculations, and its performance was comparable with the corresponding GPUs. Its main advantages were the built-in 512-bit vector registers and the ease of transferring existing codes from traditional x86 architectures. In the article, we move the code developed for a standard CPU to the coprocessor. We compareits performance with our OpenCL implementation of the numerical integration algorithm, previously developed for GPUs. The GPU code is tuned to fit into a coprocessor by ourauto-tuning mechanism. Tests included two types of tasks to solve, using two types of approximation and two types of elements. The obtained timing results allow comparing the performance of highly optimized CPU and GPU codes with a Xeon Phi coprocessor performance. This article answers whether such massively parallel architectures perform better using the CPU or GPU programming method. Furthermore, we have compared the Xeon Phi architecture and the latest available Intel’s i9 13900K CPU when writing this article. This comparison determines if the old Xeon Phi architecture remains competitive in today’s computing landscape. Our findings provide valuable insights for selectingthe most suitable hardware for numerical computations and the appropriate algorithmic design.