A new algorithm for computing global resolvent modes in a CPU and memory efficient manner

Resolvent (or input-output) analysis has proven to be a useful tool for understanding and modeling turbulent flows. In particular, the leading singular vectors of the resolvent operator provide insight into energy amplification mechanisms and coherent structures. However, standard algorithms for computing singular modes of the resolvent operator scale poorly with problem size, hindering application to many flows of interest, especially three-dimensional ones. Recent methods using randomized singular value decomposition (RSVD) have reduced computational cost but still contain bottlenecks for large systems. We combine the RSVD algorithm with an efficient time-stepping method that exploits the direct and adjoint time-domain equations underlying the resolvent system to overcome these bottlenecks. We show that our algorithm scales linearly with problem size, drastically reducing CPU and memory costs for large systems. Moreover, our algorithm simultaneously computes the resolvent modes for a range of frequencies. In this talk, we illustrate the efficacy of our algorithm by applying it to two- and three-dimensional jets.