Numerical solution and accelerated computations for a radiative transfer equation in stellar atmospheres

• Type: Another Publication in an International Scientific Journal
• Date: 2025

Authors

vasconcelos, pb (Author) FEP; Fernandes, R (Author) Other; Filomena Dias d Almeida (Author) FEUP

Journal

Title: Integral Transforms and Special Functions

Pages: 1-19

ISSN: 1065-2469

Publisher: Taylor & Francis

Indexing

ISI Web of Knowledge - 0 Citations

Scopus - 0 Citations

Other information

Authenticus ID: P-01A-JB2

DOI: 10.1080/10652469.2025.2590581

Abstract (EN): This paper presents a reframed and critically examined review of key contributions to the numerical treatment of radiative transfer problems in stellar atmospheres, formulated as second-kind Fredholm integral equations with weakly singular kernel. In addition to revisiting foundational analytical approaches, the study emphasizes advanced numerical implementation strategies and presents novel computational results, particularly those leveraging parallel computing architectures. The problem is discretized using projection methods based on piecewise constant functions, yielding finite-dimensional linear systems. Achieving high-precision solutions often entails solving large-scale systems with challenging condition numbers. To mitigate these difficulties, iterative refinement techniques are employed to improve initial approximations through progressively finer discretizations and sparsity techniques to efficiently handle and process large and sparse data structures. Special attention is devoted to optimizing computational efficiency, including the assessment of parallel algorithms and results demonstrate substantial reductions in computation time when solving large, sparse systems. The paper also explores the application of these techniques to spectral computations, highlighting the potential of parallel architectures to enhance both precision and scalability in astrophysical modelling.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 19