  Scale analysis based on coarse-graining has been proposed recently as an
alternative to Fourier analysis. It is now broadly used to analyze energy
spectra and energy transfers in eddy-resolving ocean simulations. However, for
data from unstructured-mesh models it requires interpolation to a regular grid.
We present a high-performance Python implementation of an alternative
coarse-graining method which relies on implicit filters using discrete
Laplacians. This method can work on arbitrary (structured or unstructured)
meshes and is applicable to the direct output of unstructured-mesh ocean
circulation atmosphere models. The computation is split into two phases:
preparation and solving. The first one is specific only to the mesh. This
allows for auxiliary arrays that are then computed to be reused, significantly
reducing the computation time. The second part consists of sparse matrix
algebra and solving linear system. Our implementation is accelerated by GPUs to
achieve unmatched performance and scalability. This results in processing data
based on meshes with more than 10M surface vertices in a matter of seconds. As
an illustration, the method is applied to compute spatial spectra of ocean
currents from high-resolution FESOM2 simulations.
