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A Parallel Implementation of the Atkinson Algorithm for Solving a Fredholm Equation

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Book cover High Performance Computing for Computational Science — VECPAR 2002 (VECPAR 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2565))

Abstract

In this paper we study the parallelization of the Atkinson iterative refinement method. This algorithm will be used in conjunction with a projection method to produce an approximate solution of a radiation transfer problem in Astrophysics. The transfer problem is modelled via a Fredholm integral equation of the second kind with weakly singular kernel.

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References

  1. Ahues, M., D'Almeida, F.D., Largillier, A., Titaud, O., Vasconcelos, P.: An L1 Refined Projection Approximate Solution of the Radiative Transfer Equation in Stellar Atmospheres. Journal of Computational and Apllied Mathematics 140 (2002) 13–26 369, 370

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  3. Abramowitz, M., Stegun, I. A.: Handbook of Mathematical Functions. Dover, New York (1965) 369

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  4. Ahues, M., D'Almeida, F.D., Largillier, A., Titaud, O., Vasconcelos, P.: Iterative Refinement Schemes for an Ill-Conditioned Transfer Equation in Astrophysics. Algorithms for Approximation IV 33 (2002) 70–77 370

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  5. Ahues, M., Largillier, A., Titaud, O.: The roles of a weak singularity and the grid uniformity in the relative error bounds. Numer. Funct. Anal. and Optimiz., 22 (2001) 789–814 370

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Author information

Authors and Affiliations

  1. Faculdade Engenharia Univ. Porto, Rua Dr. Roberto Frias, 4200-465, PORTO, Portugal

    Filomena Dias d’Almeida

  2. Faculdade Economia Univ. Porto, Rua Dr. Roberto Frias, 4200-464, PORTO, Portugal

    Paulo Beleza Vasconcelos

Authors
  1. Filomena Dias d’Almeida
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  2. Paulo Beleza Vasconcelos
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Editor information

Editors and Affiliations

  1. Faculdade de Engenharia da, Universidade do Porto, Rua Dr. Roberto Frias, 4200-465, Porto, Portugal

    José M. L. M. Palma  & A. Augusto Sousa  & 

  2. Department of Computer Science, University of Tennessee, 37996-1301, Knoxville, TN, USA

    Jack Dongarra

  3. Departamento de Sistemas Informáticos y Computación, Universidad Politécnica de Valencia, Camino de Vera, s/n, Apartado 22012, 46020, Valencia, Spain

    Vicente Hernández

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© 2003 Springer-Verlag Berlin Heidelberg

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d’Almeida, F.D., Vasconcelos, P.B. (2003). A Parallel Implementation of the Atkinson Algorithm for Solving a Fredholm Equation. In: Palma, J.M.L.M., Sousa, A.A., Dongarra, J., Hernández, V. (eds) High Performance Computing for Computational Science — VECPAR 2002. VECPAR 2002. Lecture Notes in Computer Science, vol 2565. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36569-9_24

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  • DOI: https://doi.org/10.1007/3-540-36569-9_24

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00852-1

  • Online ISBN: 978-3-540-36569-3

  • eBook Packages: Springer Book Archive

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