Skip to main content

Parallel Finite Element Simulation of 3D Mold-Filling Problems

  • Chapter
High Performance Computing Systems and Applications

Part of the book series: The International Series in Engineering and Computer Science ((SECS,volume 541))

  • 248 Accesses

Abstract

This paper presents a distributed memory parallel implementation of a three dimensional stabilized finite element solver for industrial mold-filling problems using the MPI standard library. These problems present unusual challenges for both the physical modeling and parallelization. Numerical methods and algorithms are proposed for parallel system generation, assembly and linear system solve. Results show that the stabilized formulation is accurate, efficient and leads to linear systems that can be solved very efficiently using simple BiCGStab solver with local ILU(0) preconditioner. Results also show that the proposed approach and data structure are reasonably efficient up to 16 CPUs.

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
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover 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.

Similar content being viewed by others

References

  • Audet, M., Hétu, J.-F., and Ilinca, F. (1998). Application of a parallel algorithm to 3-d mold filling and solidification processes. In TMS, editor, Modeling of Casting, Welding and Advanced Solidification Processes-VIII, pages 29–36.

    Google Scholar 

  • der Vorst, H. V. (1992). Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems. SIAM Journal of Scientific and Statistical Computing, 13:631–644.

    MATH  Google Scholar 

  • Franca, L. P. and Frey, S. L. (1992). Stabilized finite element methods: II. The incompressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering, 99:209–233.

    Article  MathSciNet  Google Scholar 

  • Franca, L. P. and Hughes, T. J. R. (1993). Convergence analyses of Galerkin-least-squares methods for symmetric advective-diffusive forms of the Stokes and incompressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering, 105:285–298.

    MathSciNet  Google Scholar 

  • Hétu, J.-F. and Ilinca, F. (1997). 3D GLS finite element formulation applied to mold-filling and solidification processes. In Tenth International Conference on Numerical Methods for Thermal Problems, Swansea, UK.

    Google Scholar 

  • Hughes, T. J. R. and Brooks, A. N. (1982). A theoretical framework for Petrov-Galerkin methods with discontinuous weighting functions: Application to the streamline upwind procedure. In et al., R. H. G., editor, Finite Elements in Fluids, volume IV. Wiley, Chichester.

    Google Scholar 

  • Hughes, T. J. R., Franca, L. P., and Balestra, M. (1986). A new finite element formulation for computational fluid dynamics: V. Circumventing the Babuška-Brezzi condition: A stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolations. Computer Methods in Applied Mechanics and Engineering, 59:85–99.

    Article  MathSciNet  Google Scholar 

  • Hughes, T. J. R., Franca, L. P., and Hulbert, G. M. (1989). A new finite element formulation for computational fluid dynamics: VII.’ The Galerkin-Least-Squares method for advective-diffusive equations. Computer Methods in Applied Mechanics and Engineering, 73:173–189.

    Article  MathSciNet  Google Scholar 

  • Karypis, G. and Kumar, V. (1995). A fast and high quality multilevel scheme for partitioning irregular graphs. Technical Report TR 95-035, Department of Computer Science, University of Minnesota.

    Google Scholar 

  • Saad, Y. (1996). Iterative Methods for Sparse Linear Systems. PWS Publishing Company, Boston, MA, first edition.

    Google Scholar 

  • Tezduyar, T. E., Shih, R., Mittal, S., and Ray, S. E. (1990). Incompressible flow using stabilized bilinear and linear equal-order-interpolation velocity-pressure elements. Research Report UMSI 90/165, University of Minnesota / Supercomputer Institute, Minneapolis.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Kluwer Academic Publishers

About this chapter

Cite this chapter

Audet, M., Hétu, JF., Ilincahetu, F., Bramley, R. (2002). Parallel Finite Element Simulation of 3D Mold-Filling Problems. In: Pollard, A., Mewhort, D.J.K., Weaver, D.F. (eds) High Performance Computing Systems and Applications. The International Series in Engineering and Computer Science, vol 541. Springer, Boston, MA. https://doi.org/10.1007/0-306-47015-2_53

Download citation

  • DOI: https://doi.org/10.1007/0-306-47015-2_53

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-7923-7774-0

  • Online ISBN: 978-0-306-47015-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics