Abstract
This note describes an implementation of a discontinuous Petrov Galerkin (DPG) method for acoustic waves within the framework of high order finite elements provided by the software package NGSolve. A technique to impose the impedance boundary condition weakly is indicated. Numerical results from this implementation show that a multiplicative Schwarz algorithm, with no coarse solve, provides a p-preconditioner for solving the DPG system. The numerical observations suggest that the condition number of the preconditioned system is independent of the frequency k and the polynomial degree p.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
D. Broersen, R. Stevenson, A Petrov-Galerkin discretization with optimal test space of a mild-weak formulation of convection-diffusion equations in mixed form. IMA J. Numer. Anal. doi:10.1093/imanum/dru003. (2014, to appear in print )
L. Demkowicz, J. Gopalakrishnan, A class of discontinuous Petrov-Galerkin methods. Part II: optimal test functions. Numer. Methods Partial Differ. Equ. 27, 70–105 (2011)
L. Demkowicz, J. Gopalakrishnan, I. Muga, J. Zitelli, Wavenumber explicit analysis for a DPG method for the multidimensional Helmholtz equation. Comput. Methods Appl. Mech. Eng. 213/216, 126–138 (2012)
L. Demkowicz, J. Gopalakrishnan, A primal DPG method without a first-order reformulation. Comput. Math. Appl. 66, 1058–1064 (2013)
J. Gopalakrishnan, Five lectures on DPG methods (2013). ar**V: 1306.0557
P. Monk, J. Schöberl, A. Sinwel, Hybridizing Raviart-Thomas elements for the Helmholtz equation. Electromagnetics 30, 149–176 (2010)
J. Schöberl, NETGEN – an advancing front 2D/3D-mesh generator based on abstract rules. Comput. Visual. Sci. 1, 41–52 (1997)
J. Schöberl, NGSolve [Computer Software]. Retrieved from http://sourceforge.net/projects/ngsolve/ (2014)
Acknowledgements
The authors wish to thank graduate student Lukas Kogler for his assistance in develo** an initial version of the DPG code. This work was partially supported by the NSF under grant DMS-1318916 and by the AFOSR under grant FA9550-12-1-0484.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Gopalakrishnan, J., Schöberl, J. (2015). Degree and Wavenumber [In]dependence of Schwarz Preconditioner for the DPG Method. In: Kirby, R., Berzins, M., Hesthaven, J. (eds) Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014. Lecture Notes in Computational Science and Engineering, vol 106. Springer, Cham. https://doi.org/10.1007/978-3-319-19800-2_22
Download citation
DOI: https://doi.org/10.1007/978-3-319-19800-2_22
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-19799-9
Online ISBN: 978-3-319-19800-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)