Abstract
We analyze the global convergence properties of the filtered spherical harmonic (FPN) equations for radiation transport. The well-known spherical harmonic (PN) equations are a spectral method (in angle) for the radiation transport equation and are known to suffer from Gibbs phenomena around discontinuities. The filtered equations include additional terms to address this issue that are derived via a spectral filtering procedure. We show explicitly how the global L2 convergence rate (in space and angle) of the spectral method to the solution of the transport equation depends on the smoothness of the solution (in angle only) and on the order of the filter. The results are confirmed by numerical experiments. Numerical tests have been implemented in MATLAB and are available online.
| Original language | English |
|---|---|
| Pages (from-to) | 1443-1465 |
| Number of pages | 23 |
| Journal | Communications in Mathematical Sciences |
| Volume | 14 |
| Issue number | 5 |
| DOIs | |
| State | Published - 2016 |
Funding
The submitted manuscript has been authored, in part, by a contractor of the U.S. Government under Contract No. DE-AC05-00OR22725. Accordingly, the U.S. Government retains a non-exclusive, royaltyfree license to publish or reproduce the published form of this contribution, or allow others to do so, for U.S. Government purposes. This material is based, in part, upon work supported by the National Science Foundation under Grant No. 1217170 and by NSF RNMS (KI-Net) Grant No. 11-07291.
Keywords
- Radiation transport
- Spectral filtering
- Spherical harmonics