Developments in Overlapping Schwarz Preconditioning of High-Order Nodal Discontinuous Galerkin Discretizations
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- Olson L.N., Hesthaven J.S., Wilcox L.C. (2007) Developments in Overlapping Schwarz Preconditioning of High-Order Nodal Discontinuous Galerkin Discretizations. In: Widlund O.B., Keyes D.E. (eds) Domain Decomposition Methods in Science and Engineering XVI. Lecture Notes in Computational Science and Engineering, vol 55. Springer, Berlin, Heidelberg
Recent progress has been made to more robustly handle the increased complexity of high-order schemes by focusing on the local nature of the discretization. This locality is particularly true for many Discontinuous Galerkin formulations and is the focus of this paper. The contributions of this paper are twofold. First, novel observations regarding various flux representations in the discontinuous Galerkin formulation are highlighted in the context of overlapping Schwarz methods. Second, we conduct additional experiments using high-order elements for the indefinite Helmholtz equation to expose the impact of overlap.
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