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Adaptive full domain covering meshes for parallel finite element computations

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In this work, we present a new parallelization concept for adaptive finite element methods. Compared to classical domain decomposition approaches, the concept of adaptive full domain covering meshes reduces the parallel communication overhead. Furthermore, it provides an easy way to transform sequential codes into parallel software by changing only a few lines of source code.

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References

  • Bank R.E. and Holst M. (2003). A new paradigm for parallel adaptive meshing algorithms. SIAM Rev 45(2): 291–323

    Article  MATH  MathSciNet  Google Scholar 

  • Mitchell W.F. (2004). Parallel adaptive multilevel methods with full domain partitions. Appl Num Anal Comput Math 1: 36–48

    Article  MATH  Google Scholar 

  • Vey S. and Voigt A. (2007). Amdis – adaptive multi-dimensional simulations. Comput Visual Sci 10: 57–67

    Article  Google Scholar 

  • Schmidt, A., Siebert, K. G.: Design of adaptive finite element software. LNCSE, vol. 42. Springer, Heidelberg (2005)

  • Ribalta, A., Vey, S., Voigt, A.: Error reduction in adaptive full domain covering meshes for parallel computing. Num Math (in review)

  • Schloegel K., Karypis G. and Kumar V. (2002). Parallel static and dynamic multi-constraint graph partitioning. Concurrency and Computation: Practice Experience 14: 219–240

    Article  MATH  Google Scholar 

  • Babuska I. and Melenk J.M. (1997). The partition of unity method. Int J Numer Meth Engng 40: 727–758

    Article  MATH  MathSciNet  Google Scholar 

  • Holst, M.: Applications of domain decomposition and partition of unity methods in physics and geometry. Proc. 14th Int. Conf. on Domain Decomposition Methods, pp. 63–78, 2002

  • Backofen, R., Rätz, A., Voigt, A.: Nucleation and growth in a phase field crystal (PFC) model. Phil Mag (in review)

  • Barrett J.W. and Blowey J.F. (1999). Finite element approximation of the Cahn–Hilliard equation with concentration dependent mobility. Math Comput 68: 487–517

    Article  MATH  MathSciNet  Google Scholar 

  • Kim J., Kang K.K. and Lowengrub J. (2004). Conservative multigrid methods for Cahn–Hilliard fluids. J Comput Phys 193(2): 511–543

    Article  MATH  MathSciNet  Google Scholar 

  • Feng X.B. and Prohl A. (2005). Numerical analysis of the Cahn–Hilliard equation and approximation for the Hele–Shaw problem. Interfaces Free Bound 7(1): 1–28

    MATH  MathSciNet  Google Scholar 

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Correspondence to S. Vey.

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Vey, S., Voigt, A. Adaptive full domain covering meshes for parallel finite element computations. Computing 81, 53–75 (2007). https://doi.org/10.1007/s00607-007-0243-1

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  • DOI: https://doi.org/10.1007/s00607-007-0243-1

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