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The reproducing singularity particle shape functions for problems containing singularities

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Abstract

In this paper, we construct particle shape functions that reproduce singular functions as well as polynomial functions. We also construct piecewise polynomial convolution partition of unity functions by taking the convolution of the scaled conical window function with the characteristic functions of quadrangular patches (we provide the computer code for this construction). We demonstrate that the reproducing singular particle shape functions yield highly accurate numerical solutions for the singularity problems with crack singularity or a jump boundary data singularity.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC, 28223, USA

    Hae-Soo Oh & Jae Woo Jeong

  2. Department of Mathematics, Kangwon National University, Chunchon, 200-701, South Korea

    June G. Kim

Authors
  1. Hae-Soo Oh
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  2. Jae Woo Jeong
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  3. June G. Kim
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Corresponding author

Correspondence to Hae-Soo Oh.

Additional information

H.-S. Oh was supported in part by funds provided by the University of North Carolina at Charlotte. J. G. Kim was supported in part by the Research Grant of the Kangwon National University. J. G. Kim is a Visiting Professor of the University of North Carolina at Charlotte.

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Oh, HS., Jeong, J.W. & Kim, J.G. The reproducing singularity particle shape functions for problems containing singularities. Comput Mech 41, 135–157 (2007). https://doi.org/10.1007/s00466-007-0174-x

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  • DOI: https://doi.org/10.1007/s00466-007-0174-x

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