Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2015, Article ID 147286, 7 pages
http://dx.doi.org/10.1155/2015/147286
Research Article

A PETSc-Based Parallel Implementation of Finite Element Method for Elasticity Problems

College of Mechanics and Materials, Hohai University, 1 Xikang Road, Nanjing 210098, China

Received 18 September 2014; Accepted 1 December 2014

Academic Editor: Chenfeng Li

Copyright © 2015 Jianfei Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. O. C. Zienkiewicz, R. L. Taylor, and J. Z. Zhu, The Finite Element Method: Its Basis and Fundamentals, Butterworth-Heinemann, Oxford, UK, 6th edition, 2005.
  2. M. A. Heroux, P. Vu, and C. Yang, “A parallel preconditioned conjugate gradient package for solving sparse linear systems on a Cray Y-MP,” Applied Numerical Mathematics, vol. 8, no. 2, pp. 93–115, 1991. View at Publisher · View at Google Scholar · View at Scopus
  3. A. R. M. Rao, “MPI-based parallel finite element approaches for implicit nonlinear dynamic analysis employing sparse PCG solvers,” Advances in Engineering Software, vol. 36, no. 3, pp. 181–198, 2005. View at Publisher · View at Google Scholar · View at Scopus
  4. Y. Liu, W. Zhou, and Q. Yang, “A distributed memory parallel element-by-element scheme based on Jacobi-conditioned conjugate gradient for 3D finite element analysis,” Finite Elements in Analysis and Design, vol. 43, no. 6-7, pp. 494–503, 2007. View at Publisher · View at Google Scholar · View at Scopus
  5. S. Balay, S. Abhyankar, M. F. Adams et al., PETSc Web page, 2014, http://www.mcs.anl.gov/petsc.
  6. Y. Saad, Iterative Methods for Sparse Linear Systems, SIAM, Philadelphia, Pa, USA, 2nd edition, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  7. F. H. Lee, K. K. Phoon, K. C. Lim, and S. H. Chan, “Performance of Jacobi preconditioning in Krylov subspace solution of finite element equations,” International Journal for Numerical and Analytical Methods in Geomechanics, vol. 26, no. 4, pp. 341–372, 2002. View at Publisher · View at Google Scholar · View at Scopus
  8. G. Bencheva and S. Margenov, “Parallel incomplete factorization preconditioning of rotated linear FEM system,” Journal of Computational and Applied Mechanics, vol. 4, no. 2, pp. 105–117, 2003. View at Google Scholar · View at MathSciNet
  9. S. C. Brenner, “Two-level additive Schwarz preconditioners for nonconforming finite element methods,” Mathematics of Computation, vol. 65, no. 215, pp. 897–921, 1996. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. P. T. Lin, J. N. Shadid, M. Sala, R. S. Tuminaro, G. L. Hennigan, and R. J. Hoekstra, “Performance of a parallel algebraic multilevel preconditioner for stabilized finite element semiconductor device modeling,” Journal of Computational Physics, vol. 228, no. 17, pp. 6250–6267, 2009. View at Publisher · View at Google Scholar · View at Scopus
  11. S. Balay, S. Abhyankar, M. F. Adams et al., “PETSc users manual,” Tech. Rep. ANL-95/11, Revision 3.5, Argonne National Laboratory, 2014. View at Google Scholar
  12. W. L. Briggs, V. E. Henson, and S. F. McCormick, A Multigrid Tutorial, SIAM, 2nd edition, 2000.