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Integral Methods in Science and Engineering, Volume 2 pp 105–113Cite as

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An Acceleration Approach for Fracture Problems in the Extended Boundary Element Method (XBEM) Framework

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Abstract

In this paper we investigate the use of the adaptive cross approximation (ACA) in the extended boundary element method (XBEM) framework. The proposed XBEM formulation is an implicit enrichment approach, where the stress intensity factors (SIF) are obtained with the displacements, eliminating the need of further post-processing to calculate these parameters. However, it is known that the boundary element formulation has drawbacks with respect to the matrix of the linear system of equations. Such matrices are unsymmetric and fully populated, which can be computationally expensive for large fracture problems containing multiple boundaries. We will show that ACA has the potential to accelerate the computational time without reducing the accuracy of the solution.

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Acknowledgements

The first author acknowledges the Faculty of Science, Durham University, for his Postdoctoral Research Associate funding.

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Authors and Affiliations

  1. School of Engineering and Computing Sciences, Durham University, Durham, UK

    G. Hattori, S. H. Kettle & J. Trevelyan

  2. Federal University of Espírito Santo, Av. Fernando Ferrari, 514 - Goiabeiras, Vitória, ES, 29075-910, Brazil

    L. Campos

  3. Department of Mechanical Engineering, University of Brasilia, Brasilia, Brazil

    E. L. Albuquerque

Authors
  1. G. Hattori
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  2. S. H. Kettle
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  3. L. Campos
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  4. J. Trevelyan
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  5. E. L. Albuquerque
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Corresponding author

Correspondence to G. Hattori .

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Editors and Affiliations

  1. Department of Mathematics, The University of Tulsa, Tulsa, Oklahoma, USA

    Christian Constanda

  2. Department of Mathematics, The University of Tulsa, Tulsa, Oklahoma, USA

    Matteo Dalla Riva

  3. Department of Mathematics, University of Padova, Padova, Italy

    Pier Domenico Lamberti

  4. Systems Analysis, Prognosis and Control, Fraunhofer Institute for Industrial Math, Kaiserslautern, Germany

    Paolo Musolino

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Hattori, G., Kettle, S.H., Campos, L., Trevelyan, J., Albuquerque, E.L. (2017). An Acceleration Approach for Fracture Problems in the Extended Boundary Element Method (XBEM) Framework. In: Constanda, C., Dalla Riva, M., Lamberti, P., Musolino, P. (eds) Integral Methods in Science and Engineering, Volume 2. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-59387-6_11

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