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The paper presents investigations on the implementation and performance ofthe finite element numerical integration algorithm for first orderapproximations and three processor architectures, popular in scientificcomputing, classical CPU, Intel Xeon Phi and NVIDIA Kepler GPU. A unifyingprogramming model and portable OpenCL implementation is considered for allarchitectures. Variations of the algorithm due to different problems solved anddifferent element types are investigated and several optimizations aimed atproper optimization and mapping of the algorithm to computer architectures aredemonstrated. Performance models of execution are developed for differentprocessors and tested in practical experiments. The results show the varyinglevels of performance for different architectures, but indicate that thealgorithm can be effectively ported to all of them. The general conclusion isthat the finite element numerical integration can achieve sufficientperformance on different multi- and many-core architectures and should notbecome a performance bottleneck for finite element simulation codes. Specificobservations lead to practical advises on how to optimize the kernels and whatperformance can be expected for the tested architectures.

Finite element numerical integration for first order approximations on multi-core architectures