Sketch-Based Resolvent Analysis

A significant hurdle in the adoption of resolvent analysis is the singular value decomposition (SVD) of the large linear operators involved. A matrix sketching algorithm is used to extract the primary forcing and response modes, with their associated gain. The formulation of an iterative algorithm is shown to be able to calculate the SVD of the resolvent operator with greater accuracy. The sources of error due to the selection of a test vector are discussed and it is shown that an accurate calculation of the forcing and response modes can be obtained by utilizing a test vector corresponding to a single point. The strength of this algorithm is shown by calculating the resolvent modes for a flow over a NACA 0012 airfoil at a Reynolds number of 23,000. This method is shown to converge for an arbitrary selection of test vector, obtaining results in agreement with past studies of this flow.