On perfectly matched layers for discontinuous Petrov-Galerkin methods
For computational scientists solving wave propagation problems in unbounded domains, this work provides a new DPG-PML formulation that is more physically natural and numerically verified.
The paper derives discontinuous Petrov-Galerkin methods with perfectly matched layers for wave propagation in unbounded domains, demonstrating efficacy through numerical experiments in 2D and 3D acoustic, elastic, and electromagnetic problems.
In this article, several discontinuous Petrov-Galerkin (DPG) methods with perfectly matched layers (PMLs) are derived along with their quasi-optimal graph test norms. Ultimately, two different complex coordinate stretching strategies are considered in these derivations. Unlike with classical formulations used by Bubnov-Galerkin methods, with so-called ultraweak variational formulations, these two strategies in fact deliver different formulations in the PML region. One of the strategies, which is argued to be more physically natural, is employed for numerically solving two- and three-dimensional time-harmonic acoustic, elastic, and electromagnetic wave propagation problems, defined in unbounded domains. Through these numerical experiments, efficacy of the new DPG methods with PMLs is verified.