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Sapphire++
v1.3.0-4-gbe09da0 |
A. Achterberg and K. M. Schure. A more accurate numerical scheme for diffusive shock acceleration. Monthly Notices of the Royal Astronomical Society, 411(4):2628–2636, 03 2011.
A. R. Bell, K. M. Schure, and B. Reville. Cosmic ray acceleration at oblique shocks. Monthly Notices of the Royal Astronomical Society, 418(2):1208–1216, 12 2011.
Bernardo Cockburn. An introduction to the Discontinuous Galerkin method for convection-dominated problems, pages 150–268. Springer, 1998.
F. J. B. Dann. Investigating the time-dependence of astrophysical diffusive shock acceleration using the particle transport code Sapphire++. Bachelor’s thesis, Ruprecht-Karls-Universität, 2025.
Daniele Antonio Di Pietro and Alexandre Ern. Mathematical Aspects of Discontinuous Galerkin Methods, volume 69 of Mathématiques et Applications. Springer-Verlag, Berlin Heidelberg, 2012.
L. O’C Drury. An introduction to the theory of diffusive shock acceleration of energetic particles in tenuous plasmas. Reports on Progress in Physics, 46(8):973–1027, 08 1983.
L. O. Drury. Time-dependent diffusive acceleration of test particles at shocks. Monthly Notices of the Royal Astronomical Society, 251(2):340–350, 07 1991.
M. A. Forman and L. O. Drury. Time-dependent shock acceleration: Approximations and exact solutions. In Proceedings from the 18th International Cosmic Ray Conference, volume 2, pages 267–270.
C. Kristopher Garrett and Cory D. Hauck. On the eigenstructure of spherical harmonic equations for radiative transport. Computers & Mathematics with Applications, 72(2):264–270, 2016. The Proceedings of ICMMES 2014.
Jan S. Hesthaven and Tim Warburton. Nodal Discontinuous Galerkin Methods, volume 54 of Texts in Applied Mathematics. Springer, New York, 1 edition, 2008.
John G. Kirk. Particle acceleration. In A. O. Benz and T. J.-L. Courvoisier, editors, Plasma Astrophysics, volume 24 of Saas-Fee Advanced Course, chapter 3, pages 225–314. Springer-Verlag, Berlin, Heidelberg, 1 edition, 1994.
Nils Walter Schween and Brian Reville. Using spherical harmonics to solve the Boltzmann equation: an operator-based approach. Monthly Notices of the Royal Astronomical Society, 02 2024.
Nils W. Schween, Florian Schulze, and Brian Reville. Sapphire++: A particle transport code combining a spherical harmonic expansion and the discontinuous galerkin method. Journal of Computational Physics, 523:113690, 2025.
Asma Shirin T, Brian Reville, Nils W. Schween, Florian Schulze, and John G. Kirk. Spectral curvature and breaks from fermi acceleration at oblique shocks. Monthly Notices of the Royal Astronomical Society, 11 2025.