Abstract
In this paper we explore the viability of using nodal discontinuous Galerkin methods as implemented in the software library Nudg++ [1] to compute the space charge field of an electron or positron bunch. We will use a benchmark problem to evaluate this method by comparing results from this scheme with solutions obtained analytically.
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
Preview
Unable to display preview. Download preview PDF.
References
Nunn, N., Warburton, T.: Nudg++: a nodal unstructured Discontinuous Galerkin framework. Online document (2008). URL http://www.nudg.org/. Cited Oct 10 2008
Reed, W., Hill, T.: Triangular mesh methods for the neutron transport equation. Tech. report LA-UR-73-479, Los Alamos Scientific Laboratory (1973)
DESY, Hamburg, Germany: Das europäische Röntgenlaserprojekt XFEL (2005)
Various: What is the ILC? (2008). URL http://www.linearcollider.org/
Jacobs, G.B., Hesthaven, J.S.: Implicit-explicit time integration of a high-order particle-in-cell method with hyperbolic divergence cleaning. submitted to Elsevier (2008)
Hesthaven, J., Warburton, T.: Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications, Texts in Applied Mathematics, vol. 54. Springer Verlag, New York (2008)
Warburton, T.: An explicit construction for interpolation nodes on the simplex. Journal of Engineering Mathematics 56, 247–262 (2006)
Arnold, D.N., Brezzi, F., Cockburn, B., Marini, D.: Discontinuous galerkin methods for elliptic problems
Pöplau, G., van Rienen, U.: A self-adaptive multigrid technique for 3D space charge calculations. IEEE Transactions on Magnetics 44(4), to appear (2008)
Schöberl, J.: Netgen - automatic mesh generator. Online document (2008). URL http://www.mathcces.rwth-aachen.de/netgen/. Cited Oct 10 2008
Hoppe, R.H.W., Kanschat, G., Warburton, T.: Convergence analysis of an adaptive interior penalty discontinuous galerkin method. SIAM J. Numer. Anal. p. to appear (2008)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bahls, C.R., Pöplau, G., van Rienen, U. (2010). Using Nudg++ to Solve Poisson’s Equation on Unstructured Grids. In: Roos, J., Costa, L. (eds) Scientific Computing in Electrical Engineering SCEE 2008. Mathematics in Industry(), vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12294-1_13
Download citation
DOI: https://doi.org/10.1007/978-3-642-12294-1_13
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-12293-4
Online ISBN: 978-3-642-12294-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)