An efficient long-time integrator for Chandrasekhar equations

A drawback of using Chandrasekhar equations for regulator problems is the need to perform long-time integration of these equations to reach a steady state. Since the equations are stiff, this long-time integration frequently defeats the computational advantages the Chandrasekhar equations have over solving the algebraic Riccati equations. In this paper, we present a strategy for approximating the long-time behavior of the Chandrasekhar equations. Our approach leverages recent developments in building accurate, empirical, reduced-order models for high-order systems. The aim here is to build a reduced-order model for the Chandrasekhar equations that is accurate near the steady state gain. We then assemble a corresponding low-dimensional Riccati equation that can be solved easily. For this study, we use the proper orthogonal decomposition (POD) to generate the reduced-order model. A heuristic for building a suitable input collection for POD is proposed. Numerical experiments using a 2D advection-diffusion-reaction (ADR) equation demonstrate the computational feasibility of our approach.