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An efficient finite element solution using a large pre-solved regular element

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Abstract

In this paper a finite element algorithm is presented using a large pre-solved hyper element. Utilizing the largest rectangle/cuboid inside an arbitrary domain, a large hyper element is developed that is solved using graph product rules. This pre-solved hyper element is efficiently inserted into the finite element formulation of partial differential equations (PDE) and engineering problems to reduce the computational complexity and execution time of the solution. A general solution of the large pre-solved element for a uniform mesh of triangular and rectangular elements is formulated for second-order PDEs. The efficiency of the algorithm depends on the relative size of the large element and the domain; however, the method remains as efficient as a classic method for even relatively small sizes. The application of the method is demonstrated using different examples.

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Authors and Affiliations

  1. Department of Biomedical Engineering, University of Kentucky, Lexington, KY, 40506, USA

    I. Shojaei

  2. Centre of Excellence for Fundamental Studies in Structural Engineering, Iran University of Science and Technology, Tehran, Iran

    A. Kaveh

  3. School of Engineering Science, College of Engineering, University of Tehran, Tehran, Iran

    H. Rahami

Authors
  1. I. Shojaei
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  2. A. Kaveh
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  3. H. Rahami
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Correspondence to A. Kaveh.

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Shojaei, I., Kaveh, A. & Rahami, H. An efficient finite element solution using a large pre-solved regular element. Acta Mech 227, 1331–1349 (2016). https://doi.org/10.1007/s00707-015-1552-7

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  • DOI: https://doi.org/10.1007/s00707-015-1552-7

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