Apply GPU to accelerate the convolution computation of signal shape and detector resolution changed with energy

[Background] The relationship of detector resolution changed with energy should be considered when the intrinsic spectra have wide range in experiments like neutrino energy measurement. The normal numerical integration method using center processing unit (CPU) does not meet the performance requirement. [Purpose] This study aims to find a method which can accelerate the convolution operation without losing convenience. [Methods] The graphics processing unit (GPU) and compute unified device architecture (CUDA) toolkit are employed to implement RooFit's probability density function (PDF) class and calculate the numerical integration parallelly. [Results] In the test server using E5-2603 v3 as CPU and K80 as GPU, this method improves the speed as high as 218 times when the integration nodes set to be 1 million. [Conclusion] Combining GPU with RooFit library can get a significant improvement in the speed without lose RooFit's convenience. The method could be an example for those experiments which need complicated convolution calculations. (authors)