Filomena Dias d'Almeida and Paulo Beleza Vasconcelos
CMUP - Centro de Matemática da Universidade do Porto
Porto, Portugal
emails: falmeida@fe.up.pt and pjv@fep.up.pt respectively
The numerical approximation and parallelization of an algorithm for the solution of a radiative transfer equation modelling the emission of photons in stellar atmospheres will be described. This is formulated in the integral form yielding a weakly singular Fredholm integral equation defined on a Banach space. The numerical solution is based on the projection of the integral operator onto a finite dimensional subspace. To obtain a good accuracy it is necessary to use a large dimension and in consequence a large algebraic linear system. The approach we use is to refine iteratively an approximate initial solution obtained by the projection onto a subspace of moderate (small) size. This iterative refinement is a Newton-type method where the resolvent operator is replaced with 3 different approximations. The main objective of this work is to report on the performance of the parallel code that includes the projection and the 3 iterative refinement formulae. In opposition to the usual integral problems, this one leads to a band sparse discretization matrix. This fact is taken in account by using sparse data handling and by a particular distribution of the matrix blocks among the processors.