Adaptive mesh refinement (AMR) plays a fundamental role in simulating particular flow phenomena that have vastly different resolution requirements throughout the computational domain. Proper orthogonal decomposition (POD), on the other hand, serves as a popular tool to extract coherent structures from the fluid data and build reduced order models. We present a new method to perform POD on AMR data sets that eliminates repeated operations that arise from using nearest neighbor interpolation of the data onto a uniform grid before performing POD. More fundamentally, we believe that this is the first algorithm to eliminate redundant operations for matrix multiplications with repeated values in each matrix.
We provide all code
amrPOD to evaluate the efficiency of the algorithm as shown in the
paper. Specifically, we stress the algorithm using synthetically generated AMR data to identify where the new algorithm out performs standard matrix operations since the new algorithm requires additional overhead of checking the grid level at various locations. Additionally, we show with genuine AMR data of an axisymmetric buoyant jet and a compiled and optimized version of the code, our algorithm reduces the CPU time. Details of how to use the code are provided in the