A Time-Adaptive Multirate Quasi-Newton Waveform Iteration for Coupled Problems

Abstract

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 behavior. 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 method's efficiency.