A time adaptive multirate Dirichlet–Neumann waveform relaxation method for heterogeneous coupled heat equations

We consider partitioned time integration for heterogeneous coupled heat equations. First and second order multirate, as well time-adaptive Dirichlet-Neumann Waveform relaxation (DNWR) methods are derived. In 1D implicit Euler integration, we analytically determine optimal parameters the fully discrete scheme. test robustness of on multirate method in 2D. DNWR is shown to be very robust consistently yielding fast convergence rates, whereas closely related Neumann-Neumann relaxtion (NNWR) slower or even diverges. The waveform approach naturally allows different timesteps subproblems. a performance comparison DNWR, dominates due automatically finding suitable stepsize ratios. Overall, obtain fast, robust, adaptive solver unsteady conjugate transfer.