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In this paper we present an optimization of a spectral finite element method implementation. The improvements consisted in the modification of the memory layout of the main algorithmic kernels and in the augmentation of the arithmetic intensity via loop transformations. The code has been deployed on multi-core SIMD machines and GPU. Compared to our starting point, i.e. the original scalar sequential code, we achieved a speed up of ×228 on CPU.We present comparisons with the SPECFEM2D code that prove the good performances of our implementation on similar cases. On GPU, a hybrid solution is investigated.

A fast implementation of a spectral finite elements method on CPU and GPU applied to ultrasound propagation