On perfectly matched layers for discontinuous Petrov-Galerkin methods

Abstract

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.

19 pages, 6 figures

References in corpus (6)

• High-order polygonal discontinuous Petrov-Galerkin (PolyDPG) methods using ultraweak formulations
• Discrete least-squares finite element methods
• Goal-oriented adaptive mesh refinement for non-symmetric functional settings
• Using a DPG method to validate DMA experimental calibration of viscoelastic materials
• Superconvergence in a DPG method for an ultra-weak formulation
• DPG* Method

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• Stability Analysis for Electromagnetic Waveguides. Part 1: Acoustic and Homogeneous Electromagnetic Waveguides