On a convergent DSA preconditioned source iteration for a DGFEM method for radiative transfer

Olena Palii*, Matthias Schlottbom*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

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Abstract

We consider the numerical approximation of the radiative transfer equation using discontinuous angular and continuous spatial approximations for the even parts of the solution. The even-parity equations are solved using a diffusion synthetic accelerated source iteration. We provide a convergence analysis for the infinite-dimensional iteration as well as for its discretized counterpart. The diffusion correction is computed by a subspace correction, which leads to a convergence behavior that is robust with respect to the discretization. The proven theoretical contraction rate deteriorates for scattering dominated problems. We show numerically that the preconditioned iteration is in practice robust in the diffusion limit. Moreover, computations for the lattice problem indicate that the presented discretization does not suffer from the ray effect. The theoretical methodology is presented for plane-parallel geometries with isotropic scattering, but the approach and proofs generalize to multi-dimensional problems and more general scattering operators verbatim.

Original languageEnglish
Pages (from-to)3366-3377
Number of pages12
JournalComputers and mathematics with applications
Volume79
Issue number12
Early online date22 Feb 2020
DOIs
Publication statusPublished - 15 Jun 2020

Keywords

  • Convergence rates
  • Diffusion synthetic acceleration
  • Discontinuous angular approximation
  • Discrete ordinates method
  • Radiative transfer

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