Adaptive QN Regularization

This page is currently a WORK IN PROGRESS. Here I will present the step-wise development of a novel "Adaptive Regularization and Secant Selection" strategy that dynamically maintains suitable conditioning of the least-squares optimization problem that underpins all quasi-newton partitioned strategies. In particular, I describe here a procedure to assess the usefulness of the collected secant data pairs as well as the efficacy of a given update step. These measures determine what secant data pairs to retain when approximating the interfacial Jacobian and thereby adaptively adjusts the weighting of a scaled regularization paramter to ensure productivity as well as residual orthogonality in the resulting fixed point update step. This novel method has been found to be particularly effective in enhancing the convergence rate as well as iterative stability of partitioned FSI simulations involving very strong added-mass effects.