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A Weakly Penalized Discontinuous Galerkin Method for Radiation in Dense, Scattering Media

Guido Kanschat and José Pablo Lucero Lorca


We review the derivation of weakly penalized discontinuous Galerkin methods for scattering dominated radiation transport and extend the asymptotic analysis to non-isotropic scattering. We focus on the influence of the penalty parameter on the edges and derive a new penalty for interior edges and boundary fluxes. We study how the choice of the penalty parameters influences discretization accuracy and solver speed.

Funding source: Deutsche Forschungsgemeinschaft

Award Identifier / Grant number: GSC 220

Funding statement: The first author was supported by the Sino-German Science Center (grant id 1228) on the occasion of the Chinese-German Workshop on Computational and Applied Mathematics in Augsburg 2015. The second author was supported by the Heidelberg Graduate School of Mathematical and Computational Methods for the Sciences (HGS MathComp), DFG grant GSC 220 in the German Universities Excellence Initiative.


Computations in this article were done using release 8.3 of the deal.II finite element library [5, 6]. Furthermore, we thank J. Ragusa and J.-L. Guermond for fruitful discussions.


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Received: 2015-12-23
Revised: 2016-5-13
Accepted: 2016-5-20
Published Online: 2016-7-6
Published in Print: 2016-10-1

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