Implementation of implicit filter for spatial spectra extraction

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, it requires interpolation to a regular mesh for data from unstructured-mesh models. We present 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 models. We also present a high-performance Python implementation of this method. In this implementation computation has been 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 computation time. The second part consists of sparse matrix algebra and solving linear system. Our implementation is accelerated by GPU 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. At present, the method is used to compute energy or power spectra of ocean flows.