Foundations of the blended isogeometric discontinuous Galerkin (BIDG) method

A new discontinuous Galerkin (DG) method is introduced that seamlessly merges exact geometry with high-order solution accuracy. This new method is called the blended isogeometric discontinuous Galerkin (BIDG) method. The BIDG method contrasts with existing high-order accurate DG methods over curvilinear meshes (e.g. classical isoparametric DG methods) in that the underlying geometry is exactly preserved at every mesh refinement level, allowing for intricate and complicated real-world mesh design to be streamlined and automated using computer-aided design (CAD) software. The BIDG method is designed specifically for easy incorporation into existing code architecture. This paper discusses specific details of implementation using two examples: (1) the acoustic wave equations, and (2) Maxwell's equations. Basic tests of accuracy and stability are demonstrated, including optimal convergence, and supplemental theoretical results are provided in the appendix along with links to fully operational working code examples.