Finite Rank Approximation based method for solving the RTE in stellar atmospheres and application to an inverse problem

Abstract

The Finite Rank Approximation (FRA) based method is well known in operator approximation theory but it is also useful for suggesting numerical methods for solving integral equations. In this document we describe two FRA methods for the numerical resolution of the integral formulation of the 1D Radiative Transfer Equation (RTE) posed in a static slab; we browse some advantages of them (especially the possibility to control the error) and we give some reduction of computation technics (iterative refinement schemes) which can be used with these methods. Numerical results obtained for a realistic Sun atmosphere model are given. In the last section we give an example of an inverse problem associated to the RTE: we show the iterative recovering of the albedo from the measurement of the outgoing specific intensity at a surface of the considered domain.