Quasi-Newton methods have proven to be an efficient way to couple partitioned solvers in fluid-structure interaction problems, as they are able to stabilize cases with high added-mass, as well as accelerate the convergence. However, these methods assume that the coupled system is a complete black-box, whereas often, its behavior is well approximated by a surrogate model. Such a model may be obtained by coarsening the system, simplifying the physics, reverting to analytical approximations or considering the system at a previous point in time. The principal idea of this work is to use an initial solution and a Jacobian provided by the surrogate model, to expedite the convergence even further. This article presents a new framework for the inclusion of surrogate models in quasi-Newton methods and positions several existing methods with respect to it.

拟牛顿方法已被证明是在流固耦合问题中耦合分区求解器的有效方法，因为它们能够稳定具有高附加质量的情况，并加速收敛。然而，这些方法假设耦合系统是一个完整的黑盒，而通常情况下，它的行为可以通过代理模型很好地近似。这样的模型可以通过粗化系统、简化物理、恢复到解析近似或在先前的时间点考虑系统来获得。这项工作的主要思想是使用代理模型提供的初始解和雅可比行列式，以进一步加速收敛。本文提出了一个新框架，用于在拟牛顿方法中包含代理模型，并就此定位了几种现有方法。