Robust Multisecant Quasi-Newton Variants for Parallel Fluid-Structure Simulations---and Other Multiphysics Applications

Multisecant quasi-Newton methods have been shown to be particularly suited to solve nonlinear fixed-point equations that arise from partitioned multiphysics simulations where the exact Jacobian is inaccessible. In all these methods, the underdetermined multisecant equation for the approximate (inverse) Jacobian is enhanced by a norm minimization condition. The standard choice is the minimization of the Frobenius norm of the approximate inverse Jacobian. In this setting, it is well known that transient fluid-structure simulations typically require the use of secant information also from previous time steps to achieve a small enough number of iterations per implicit time step. The number of these time steps highly depends on the application, the physical parameters, the used solvers, and the mesh resolution. Using too few leads to a relatively high number of iterations, while using too many leads not only to a computational overhead but also to an increase in the number of iterations as well. Determining th...