Modern physics simulations are often complex and computationally expensive. A common approach to tackle this problem involves the division of the simulation domain into smaller subdomains, which are solved separately. This domain partitioning also involves a process to recombine the partial solutions to a global one, named coupling. Different numerical methods are then available to solve the subproblems. Promising methods for this are parallel-in-time (PinT) methods, which aim to parallelize the time stepping over the temporal domain, with a promising candidate being the spectral deferred correction (SDC)-based PFASST algorithm. A combination of domain partitioning and PinT methods seems to be promising for efficient simulation parallelization. However, for the successful combination of these methods, it is desired that the interaction of both methods does not alter their error behavior significantly.
This thesis focuses on the analysis of error and convergence of an SDC-based time integrator in the context of domain partitioning. In this context, we implement a solver using SDC and carry out simulations to investigate its error behavior with different settings. For the implementation of the solver, we use the open-source libraries FEniCS and pySDC, for coupling the library preCICE is used.
We analyze the error behavior of the implemented solver for different scenarios of the forced heat equation in a two-dimensional domain and provide data and suggestions for future research.