Hybrid Transmission Conditions for the Schwarz Domain Decomposition Method for RF Accelerating Cavities

We introduce a new transmission condition for the domain decomposition method with application in particle accelerator problems. The new transmission condition combines a modal decomposition approach for guided-wave propagation with the commonly used approximate transmission conditions. This significantly improves the convergence properties of the domain decomposition method for these structures. As an important application, we consider the parallel computation of electromagnetic fields in a 1.3 GHz Tesla cavity on an HPC cluster. This example demonstrates the accuracy of the method and its improvement of computational efficiency.