Skip to main content

Performance Evaluation of a Parallel Algorithm for a Radiative Transfer Problem

  • Conference paper
Applied Parallel Computing. State of the Art in Scientific Computing (PARA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3732))

Included in the following conference series:

Abstract

The numerical approximation and parallelization of an algorithm for the solution of a radiative transfer equation modeling 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 main objective of this work is to report on the performance of the parallel code.

AMS Subject Classification: 32A55, 45B05, 65D20, 65R20, 68W10.

This work was supported by CMUP. CMUP is financed by FCT under programs POCTI and POSI from QCA III with FEDER and National funds.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions. Dover, New York (1960)

    Google Scholar 

  2. Ahues, M., d’Almeida, F.D., Largillier, A., Titaud, O., Vasconcelos, P.: An L1 Refined Projection Approximate Solution of the Radiation Transfer Equation in Stellar Atmospheres. J. Comput. Appl. Math. 140, 13–26 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  3. Ahues, M., Largillier, A., Limaye, B.V.: Spectral Computations with Bounded Operators. Chapman and Hall, Boca Raton (2001)

    Book  Google Scholar 

  4. 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(7&8), 789–814 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  5. Ahues, M., d’Almeida, F.D., Largillier, A., Titaud, O., Vasconcelos, P.: Iterative Refinement Schemes for an ill-Conditioned Transfer Equation in Astrophysics. In: Algorithms for Approximation IV, Univ. of Huddersfield, pp. 70–77 (2002)

    Google Scholar 

  6. d’Almeida, F.D., Vasconcelos, P.B.: 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.) VECPAR 2002. LNCS, vol. 2565, pp. 368–376. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  7. Atkinson, K.E.: A Survey of Numerical Methods for the Solution of Fredholm Integral Equations of the Second Kind. Society for Industrial and Applied Mathematics, Philadelphia (1976)

    MATH  Google Scholar 

  8. Blackford, L.S., Choi, J., Cleary, A., D’Azevedo, E., Demmel, J., Dhillon, I., Dongarra, J., Hammarling, S., Henry, G., Petitet, A., Stanley, K., Walker, D., Whaley, R.C.: ScaLAPACK Users’ Guide. Society for Industrial and Applied Mathematics, Philadelphia (1997)

    Book  MATH  Google Scholar 

  9. Brakhage, H.: Uber die Numeriche Bechandlung von Integralgleichungen nach der Quadraturformelmethod. Numer. Math. 2, 183–196 (1960)

    Article  MATH  MathSciNet  Google Scholar 

  10. Dongarra, J.J., Duff, I.S., Sorensen, D.C., van der Vorst, H.A.: Numerical Linear Algebra for High-Performance Computers. Society for Industrial and Applied Mathematics, Philadelphia (1998)

    Book  MATH  Google Scholar 

  11. Rutily, B.: Multiple Scattering Theoretical and Integral Equations. In: Integral Methods in Science and Engineering: Analytic and Numerical Techniques, pp. 211–231. Birkhauser, Basel (2004)

    Google Scholar 

  12. Saad, Y.: Iterative Methods for Sparse Linear Systems. PWS Publishing Company (1996)

    Google Scholar 

  13. Snir, M., Otto, S., Huss-Lederman, S., Walker, D., Dongarra, J.J.: MPI: The Complete Reference. The MIT Press, Cambridge (1996)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Vasconcelos, P.B., d’Almeida, F. (2006). Performance Evaluation of a Parallel Algorithm for a Radiative Transfer Problem. In: Dongarra, J., Madsen, K., Waśniewski, J. (eds) Applied Parallel Computing. State of the Art in Scientific Computing. PARA 2004. Lecture Notes in Computer Science, vol 3732. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11558958_104

Download citation

  • DOI: https://doi.org/10.1007/11558958_104

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-29067-4

  • Online ISBN: 978-3-540-33498-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics