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Published in:
2013 | OriginalPaper | Chapter
Preconditioning High–Order Discontinuous Galerkin Discretizations of Elliptic Problems
Authors : Paola F. Antonietti, Paul Houston
Published in: Domain Decomposition Methods in Science and Engineering XX
Publisher: Springer Berlin Heidelberg
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In recent years, attention has been devoted to the development of efficient iterative solvers for the solution of the linear system of equations arising from the discontinuous Galerkin (DG) discretization of a range of model problems. In the framework of two level preconditioners, scalable non-overlapping Schwarz methods have been proposed and analyzed for the
h
–version of the DG method in the articles [1, 2, 6, 7, 9]. Recently, in [3] it has been proved that the non-overlapping Schwarz preconditioners can also be successfully employed to reduce the condition number of the stiffness matrices arising from a wide class of high–order DG discretizations of elliptic problems. In this article we aim to validate the theoretical results derived in [3] for the multiplicative Schwarz preconditioner and for its symmetrized variant by testing their numerical performance.