Computational Mechanics

, Volume 47, Issue 3, pp 265–282

Parallel simulations of three-dimensional cracks using the generalized finite element method

Original Paper

DOI: 10.1007/s00466-010-0546-5

Cite this article as:
Kim, DJ., Duarte, C.A. & Sobh, N.A. Comput Mech (2011) 47: 265. doi:10.1007/s00466-010-0546-5


This paper presents a parallel generalized finite element method (GFEM) that uses customized enrichment functions for applications where limited a priori knowledge about the solution is available. The procedure involves the parallel solution of local boundary value problems using boundary conditions from a coarse global problem. The local solutions are in turn used to enrich the global solution space using the partition of unity methodology. The parallel computation of local solutions can be implemented using a single pair of scatter–gather communications. Several numerical experiments demonstrate the high parallel efficiency of these computations. For problems requiring non-uniform mesh refinement and enrichment, load unbalance is addressed by defining a larger number of small local problems than the number of parallel processors and by sorting and solving the local problems based on estimates of their workload. A simple and effective estimate of the largest number of processors where load balance among processors is maintained is also proposed. Several three-dimensional fracture mechanics problems aiming at investigating the accuracy and parallel performance of the proposed GFEM are analyzed.


Generalized FEM Extended FEM Parallel computation OpenMP Global–local analysis Fracture 

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of Architectural EngineeringKyung Hee UniversityYonginKorea
  2. 2.Department of Civil and Environmental EngineeringUniversity of Illinois at Urbana-Champaign, Newmark LaboratoryUrbanaUSA

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