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