We present novel coupling schemes for partitioned multi-physics simulation that combine four important aspects for strongly coupled problems: implicit coupling per time step, fast and robust acceleration of the corresponding iterative coupling, support for multi-rate time stepping, and higher-order convergence in time. To achieve this, we combine waveform relaxation -- a known method to achieve higher order in applications with split time stepping based on continuous representations of coupling variables in time -- with interface quasi-Newton coupling, which has been developed throughout the last decade and is generally accepted as a very robust iterative coupling method even for gluing together black-box simulation codes. We show convergence results (in terms of convergence of the iterative solver and in terms of approximation order in time) for two academic test cases -- a heat transfer scenario and a fluid-structure interaction simulation. We show that we achieve the expected approximation order and that our iterative method is competitive in terms of iteration counts with those designed for simpler first-order-in-time coupling.

中文翻译：

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用于分区表面耦合多物理场应用的拟牛顿波形迭代

我们提出了分区多物理场仿真的新耦合方案，该方案结合了强耦合问题的四个重要方面：每个时间步的隐式耦合、相应迭代耦合的快速和稳健加速、支持多速率时间步长和高阶收敛及时。为了实现这一点，我们将波形弛豫（一种已知的在应用中实现更高阶的方法，基于耦合变量在时间上的连续表示的分裂时间步进）与接口准牛顿耦合相结合，后者在过去十年中得到了发展和被普遍接受为一种非常健壮的迭代耦合方法，即使是将黑盒仿真代码粘合在一起也是如此。我们展示了两个学术测试案例的收敛结果（根据迭代求解器的收敛性和时间上的近似顺序）——传热场景和流固耦合模拟。我们表明我们实现了预期的近似阶数，并且我们的迭代方法在迭代次数方面与那些为更简单的一阶时间耦合而设计的方法相比具有竞争力。