Advertisement

Performance Comparison of Parallel Geometric and Algebraic Multigrid Preconditioners for the Bidomain Equations

  • Fernando Otaviano Campos
  • Rafael Sachetto Oliveira
  • Rodrigo Weber dos Santos
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3991)

Abstract

The purpose of this paper is to discuss parallel preconditioning techniques to solve the elliptic portion (since it dominates computation) of the bidomain model, a non-linear system of partial differential equations that is widely used for describing electrical activity in the heart. Specifically, we assessed the performance of parallel multigrid preconditioners for a conjugate gradient solver. We compared two different approaches: the Geometric and Algebraic Multigrid Methods. The implementation is based on the PETSc library and we reported results for a 6-node Athlon 64 cluster. The results suggest that the algebraic multigrid preconditioner performs better than the geometric multigrid method for the cardiac bidomain equations.

Keywords

Coarse Grid Multigrid Method Parallel Speedup Conjugate Gradient Iteration Parallel Geometric 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Sepulveda, N.G., Roth, B.J., Wikswo Jr., J.P.: Current injection into a two-dimensional anistropic bidomain. Biophysical J. 55, 987–999 (1989)CrossRefGoogle Scholar
  2. 2.
    Hooke, N., Henriquez, C., Lanzkron, P., Rose, D.: Linear algebraic transformations of the bidomain equations: Implications for numerical methods. Math. Biosci. 120(2), 127–145 (1994)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Weber dos Santos, R., Plank, G., Bauer, S., Vigmond, E.J.: Parallel Multigrid Preconditioner for the Cardiac Bidomain Model. IEEE Trans. Biomed. Eng. 51(11), 19601968 (2004)Google Scholar
  4. 4.
    Weber dos Santos, R., Plank, G., Bauer, S., Vigmond, E.: Preconditioning techniques for the bidomain equations. Lecture Notes In Computational Science And Engineering 40, 571–580 (2004)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Henson, V.E., Yang, U.M.: BoomerAMG: a Parallel Algebraic Multigrid Solver and Preconditioner. Technical Report UCRL-JC-139098, Lawrence Livermore National Laboratory (2000)Google Scholar
  6. 6.
    Balay, S., Buschelman, K., Gropp, W., Kaushik, D., Knepley, M., McInnes, L., Smith, B., Zhang, H.: PETSc users manual. Technical report ANL-95/11 - Revision 2.1.15, Argony National Laboratory (2002)Google Scholar
  7. 7.
    Vigmond, E., Aguel, F., Trayanova, N.: Computational techniques for solving the bidomain equations in three dimensions. Trans. Biomed. Eng. IEEE. 49, 1260–1269 (2002)CrossRefGoogle Scholar
  8. 8.
    Briggs, W., Henson, V., McCormick, S.: A Multigrid Tutorial. SIAM, Philadelphia, PA, Tech. Rep. (2000)Google Scholar
  9. 9.
    Jones, J., Vassilevski, P.: A parallel graph coloring heuristic. SIAM J. Sci. Comput. 14, 654–669 (1993)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Krassowska, W., Neu, J.C.: Effective boundary conditions for syncytial tissues. IEEE Trans. Biomed. Eng. 41, 143–150 (1994)CrossRefGoogle Scholar
  11. 11.
    ten Tusscher, K.H.W.J., Noble, D., Noble, P.J., Panfilov, A.V.: A model for human ventricular tissue. J. Physiol. 286, 1573–1589 (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Fernando Otaviano Campos
    • 1
  • Rafael Sachetto Oliveira
    • 1
  • Rodrigo Weber dos Santos
    • 1
  1. 1.FISIOCOMP: Laboratory of Computational Physiology, Department of Computer ScienceUniversidade Federal de Juiz de Fora (UFJF)Juiz de ForaBrazil

Personalised recommendations