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Partition of unity isogeometric analysis of two dimensional elliptic singular perturbation problems

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Abstract

The design basis functions on the reference domain in IGA are diversified and enhanced by extra enrichment functions and various local refinements with the use of partition of unity (PU) function with flat-top. These reconditioned and modified basis functions are pushed forward to the physical domain by the original design mapping for analysis. With this method, the corresponding stiffness matrix has a small bandwidth and local refinement is simple. Moreover, we construct the PU functions in the reference domain and then move them to a physical domain through a geometric mapping to be used for the generation of global basis functions on a physical domain. Therefore, we also have several advantages in calculating stiffness matrices and load vectors. Here we apply this method to various boundary layer problems.

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Acknowledgments

Bong Soo Jang was supported by the National Research Foundation of Korea(NRF) funded by the Ministry of Education (NRF-2014R1A1A2A16051147)

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Authors and Affiliations

  1. Department of Mathematical Sciences, Ulsan National Institute of Science and Technology, Ulsan, 44919, Republic of Korea

    Bongsoo Jang

  2. Department of Mathematics, North Greenville University, Tigerville, SC, 29688, USA

    Hyunju Kim

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

    Hae-Soo Oh & Sinae Kim

Authors
  1. Bongsoo Jang
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  2. Hyunju Kim
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  3. Hae-Soo Oh
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  4. Sinae Kim
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Correspondence to Hae-Soo Oh.

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Jang, B., Kim, H., Oh, HS. et al. Partition of unity isogeometric analysis of two dimensional elliptic singular perturbation problems. Comput Mech 58, 1019–1038 (2016). https://doi.org/10.1007/s00466-016-1330-y

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  • DOI: https://doi.org/10.1007/s00466-016-1330-y

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