Analysis of eigenvalue clustering leads to optimal scaling in numerical radiative transfer
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| Format: | Preprint |
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2026
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| author | Benedusi, Pietro Riva, Simone Belluzzi, Luca Serra-Capizzano, Stefano |
| author_facet | Benedusi, Pietro Riva, Simone Belluzzi, Luca Serra-Capizzano, Stefano |
| contents | We consider a multidimensional polychromatic radiative transfer (RT) problem, accounting for scattering processes in a general form, i.e. anisotropic (dipole) scattering with partial frequency redistribution. Given a discrete ordinates discretization, we report the corresponding matrix structures, depending on model and discretization parameters. Despite the possibly dense nature of these matrices, the use of Krylov methods is effective (especially in the matrix-free context) and robust. We propose a theoretical analysis, using the spectral tools of the symbol theory, explaining why Krylov convergence is robust w.r.t. all the discretization parameters, even in the unpreconditioned case. In fact, the compactness of the continuous operators used in the modeling leads to zero-clustered dense matrix sequences plus identity, so that the clustering at the unity of the spectra is deduced. Numerical experiments confirm the theoretical results, which have a direct application, for example, in the simulation of radiative transfer in stellar atmospheres, a key problem in astrophysical research. In general, we demonstrate that optimal scaling with respect to RT discretization parameters is expected for Krylov solution strategies. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_21958 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Analysis of eigenvalue clustering leads to optimal scaling in numerical radiative transfer Benedusi, Pietro Riva, Simone Belluzzi, Luca Serra-Capizzano, Stefano Numerical Analysis Solar and Stellar Astrophysics 85A25 35P05 65F15 65F10 65R20 We consider a multidimensional polychromatic radiative transfer (RT) problem, accounting for scattering processes in a general form, i.e. anisotropic (dipole) scattering with partial frequency redistribution. Given a discrete ordinates discretization, we report the corresponding matrix structures, depending on model and discretization parameters. Despite the possibly dense nature of these matrices, the use of Krylov methods is effective (especially in the matrix-free context) and robust. We propose a theoretical analysis, using the spectral tools of the symbol theory, explaining why Krylov convergence is robust w.r.t. all the discretization parameters, even in the unpreconditioned case. In fact, the compactness of the continuous operators used in the modeling leads to zero-clustered dense matrix sequences plus identity, so that the clustering at the unity of the spectra is deduced. Numerical experiments confirm the theoretical results, which have a direct application, for example, in the simulation of radiative transfer in stellar atmospheres, a key problem in astrophysical research. In general, we demonstrate that optimal scaling with respect to RT discretization parameters is expected for Krylov solution strategies. |
| title | Analysis of eigenvalue clustering leads to optimal scaling in numerical radiative transfer |
| topic | Numerical Analysis Solar and Stellar Astrophysics 85A25 35P05 65F15 65F10 65R20 |
| url | https://arxiv.org/abs/2602.21958 |