Waveform Relaxation with Asynchronous Time-integration

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