An L1 refined projection approximate solution of the radiation transfer equation in stellar atmospheres

Authors:
M. Ahues;F. D'Almeida;A. Largillier;O. Titaud;P. Vasconcelos
Affiliations:
Upres EA 3058, Université Jean Monnet, 23 rue Dr. Paul Michelon, 42023 Saint-Etienne, France;Faculdade de Engenharia da Universidade do Porto, 4050-123 Porto, Portugal;Upres EA 3058, Université Jean Monnet, 23 rue Dr. Paul Michelon, 42023 Saint-Etienne, France;Upres EA 3058, Université Jean Monnet, 23 rue Dr. Paul Michelon, 42023 Saint-Etienne, France;Faculdade de Economia da Universidade do Porto, Rua Dr. Roberto Frias, 4200 Porto, Portugal
Venue:
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 9th International Congress on computational and applied mathematics
Year:
2002

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Abstract

This paper deals with the numerical approximation of the solution of a weakly singular integral equation of the second kind which appears in Astrophysics. The reference space is the complex Banach space of Lebesgue integrable functions on a bounded interval whose amplitude represents the optical thickness of the atmosphere. The kernel of the integral operator is defined through the first exponential-integral function and depends on the albedo of the media. The numerical approximation is based on a sequence of piecewise constant projections along the common annihilator of the corresponding local means. In order to produce high precision solutions without solving large scale linear systems, we develop an iterative refinement technique of a low order approximation. For this scheme, parallelization of matrix computations is suitable.