ANZIAM J. 46(E) ppC290--C303, 2005.

Parallel implementation of a monotone domain decomposition algorithm for nonlinear reaction-diffusion problems

M. P. Hardy

I. Boglaev

(received 21 October 2004, revised 23 March 2005)

Abstract

Recently, a monotone iterative domain decomposition algorithm has been proposed for the numerical solution of nonlinear singularly perturbed reaction-diffusion problems. This paper describes a parallel implementation of the algorithm on a distributed memory cluster. Interprocess communication is effected by means of the MPI message passing library. For various domain decompositions, we give the convergence iteration count and execution time on up to 16 processors. The parallel scale-up of the algorithm improves as the number of mesh points is increased.

Download to your computer

Authors

M. P. Hardy
Mathematical Sciences Institute, Australian National University, Canberra, Australia. mailto:hardy@maths.anu.edu.au
I. Boglaev
Institute of Fundamental Sciences, Massey University, Palmerston North, New Zealand mailto:i.boglaev@massey.ac.nz

Published April 28, 2005. ISSN 1446-8735

References

  1. I. Boglaev. On monotone iterative methods for a nonlinear singularly perturbed reaction-diffusion problem. J. Comput. Appl. Math., 162:445--466, 2004. http://dx.doi.org/10.1016/j.cam.2004.02.010
  2. I. Boglaev and M. P. Hardy. Monotone finite difference domain decomposition algorithms and applications to nonlinear singularly perturbed reaction-diffusion problems. Adv. Difference Eqns., (in press). http://www.hindawi.com/journals/ade/forthcoming/S1687183905409048.html
  3. J. J. H. Miller, E. O'Riordan, and G. I. Shishkin. Fitted numerical methods for singular perturbation problems. World Scientific, Singapore, 1996.
  4. C. Pao. Monotone iterative methods for finite difference system of reaction-diffusion equations. Numer. Math., 46(4):571--586, 1985. http://dx.doi.org/10.1007/BF01389659
  5. Y. Saad and M. H. Schultz. {GMRES}: A generalized minimal residual method for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput., 7:856--869, 1986. http://locus.siam.org/SISC/volume-07/art_0907058.html