Formal solutions for polarized radiative transfer III. Stiffness and instability
Efficient numerical approximation of the polarized radiative transfer equation is challenging because this system of ordinary differential equations exhibits stiff behavior, which potentially results in numerical instability. This negatively impacts the accuracy of formal solvers, and small step-siz...
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| Format: | Journal article |
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American Astronomical Society
2018
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| _version_ | 1826296457744875520 |
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| author | Janett, G Paganini, A |
| author_facet | Janett, G Paganini, A |
| author_sort | Janett, G |
| collection | OXFORD |
| description | Efficient numerical approximation of the polarized radiative transfer equation is challenging because this system of ordinary differential equations exhibits stiff behavior, which potentially results in numerical instability. This negatively impacts the accuracy of formal solvers, and small step-sizes are often necessary to retrieve physical solutions. This work presents stability analyses of formal solvers for the radiative transfer equation of polarized light, identifies instability issues, and suggests practical remedies. In particular, the assumptions and the limitations of the stability analysis of Runge–Kutta methods play a crucial role. On this basis, a suitable and pragmatic formal solver is outlined and tested. An insightful comparison to the scalar radiative transfer equation is also presented. |
| first_indexed | 2024-03-07T04:16:38Z |
| format | Journal article |
| id | oxford-uuid:c9a017c1-6717-45a6-b06a-3d7ffe53d439 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T04:16:38Z |
| publishDate | 2018 |
| publisher | American Astronomical Society |
| record_format | dspace |
| spelling | oxford-uuid:c9a017c1-6717-45a6-b06a-3d7ffe53d4392022-03-27T07:00:41Z Formal solutions for polarized radiative transfer III. Stiffness and instabilityJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:c9a017c1-6717-45a6-b06a-3d7ffe53d439Symplectic Elements at OxfordAmerican Astronomical Society2018Janett, GPaganini, AEfficient numerical approximation of the polarized radiative transfer equation is challenging because this system of ordinary differential equations exhibits stiff behavior, which potentially results in numerical instability. This negatively impacts the accuracy of formal solvers, and small step-sizes are often necessary to retrieve physical solutions. This work presents stability analyses of formal solvers for the radiative transfer equation of polarized light, identifies instability issues, and suggests practical remedies. In particular, the assumptions and the limitations of the stability analysis of Runge–Kutta methods play a crucial role. On this basis, a suitable and pragmatic formal solver is outlined and tested. An insightful comparison to the scalar radiative transfer equation is also presented. |
| spellingShingle | Janett, G Paganini, A Formal solutions for polarized radiative transfer III. Stiffness and instability |
| title | Formal solutions for polarized radiative transfer III. Stiffness and instability |
| title_full | Formal solutions for polarized radiative transfer III. Stiffness and instability |
| title_fullStr | Formal solutions for polarized radiative transfer III. Stiffness and instability |
| title_full_unstemmed | Formal solutions for polarized radiative transfer III. Stiffness and instability |
| title_short | Formal solutions for polarized radiative transfer III. Stiffness and instability |
| title_sort | formal solutions for polarized radiative transfer iii stiffness and instability |
| work_keys_str_mv | AT janettg formalsolutionsforpolarizedradiativetransferiiistiffnessandinstability AT paganinia formalsolutionsforpolarizedradiativetransferiiistiffnessandinstability |