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 pro...

We present overlapping Schwarz methods for the numerical solution of two model problems of delay PDEs: the heat equation with a fixed delay term, and the heat equation with a distributed delay in the form of an integral over the past. We first analyze properties of the solutions of these PDEs and find that their dynamics is fundamentally different from that of regular time-dependent PDEs withou...