  We consider Waveform Relaxation (WR) methods for partitioned time-integration
of surface-coupled multiphysics problems. WR allows independent
time-discretizations on independent and adaptive time-grids, while maintaining
high time-integration orders. Classical WR methods such as Jacobi or
Gauss-Seidel WR are typically either parallel or converge quickly.
  We present a novel parallel WR method utilizing asynchronous communication
techniques to get both properties. Classical WR methods exchange discrete
functions after time-integration of a subproblem. We instead asynchronously
exchange time-point solutions during time-integration and directly incorporate
all new information in the interpolants. We show both continuous and
time-discrete convergence in a framework that generalizes existing linear WR
convergence theory. An algorithm for choosing optimal relaxation in our new WR
method is presented.
  Convergence is demonstrated in two conjugate heat transfer examples. Our new
method shows an improved performance over classical WR methods. In one example
we show a partitioned coupling of the compressible Euler equations with a
nonlinear heat equation, with subproblems implemented using the open source
libraries DUNE and FEniCS.
