We consider waveform iterations for dynamical coupled problems, or more specifically, PDEs that interact through a lower dimensional interface. We want to allow for the reuse of existing codes for the subproblems, called a partitioned approach. To improve computational efficiency, different and adaptive time steps in the subsolvers are advisable. Using so called waveform iterations in combination with relaxation, this has been achieved for heat transfer problems earlier. Alternatively, one can use a black box method like Quasi-Newton to improve the convergence behaviour. These methods have recently been combined with waveform iterations for fixed time steps. Here, we suggest an extension of the Quasi-Newton method to the time adaptive setting and analyze its properties. We compare the proposed Quasi-Newton method with state of the art solvers on a heat transfer test case, and a complex mechanical Fluid-Structure interaction case, demonstrating the methods efficiency.

翻译：本文研究动力学耦合问题的波形迭代方法，具体而言是研究通过低维界面相互作用的偏微分方程系统。我们期望能够复用各子问题的现有求解代码，即采用分区求解策略。为提高计算效率，建议在子求解器中采用差异化且自适应的时间步长。早期研究中已通过结合松弛技术的波形迭代方法在传热问题上实现了该目标。另一种方案是采用拟牛顿等黑箱方法来改善收敛特性。近期研究已将此类方法与固定时间步长的波形迭代相结合。本文提出将拟牛顿方法扩展至时间自适应场景，并分析其特性。通过在传热测试案例和复杂的流固耦合力学案例中与先进求解器进行对比，验证了所提方法的计算效率。