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A Finite Element Implementation in Three Dimensions

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A Finite Element Primer for Beginners

Part of the book series: SpringerBriefs in Applied Sciences and Technology ((BRIEFSAPPLSCIENCES))

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Abstract

Generally, the ability to change the boundary data quickly is very important in finite element computations. One approach to do this rapidly is via the variational penalty method.

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Notes

  1. 1.

    Representing the numerical approximation this way is simply to ease the understanding of the process. On the implementation level, one would not store the matrices in this form due to the large number of zeroes.

  2. 2.

    This is for illustration purposes only. For computational efficiency, one should not program such operations in this way. Clearly, the needless multiplication of zeros is to be avoided.

  3. 3.

    If a direct storage of the finite element storage of the stiffness matrix were attempted, the memory requirements would be \({\varvec{K}}(DOF,DOF)=DOF \times DOF\), where \(DOF\) indicates the total degrees of freedom, which for large problems, would be extremely demanding.

References

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Authors and Affiliations

  1. University of California, Berkeley, CA, USA

    Tarek I. Zohdi

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  1. Tarek I. Zohdi
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Correspondence to Tarek I. Zohdi .

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Zohdi, T.I. (2015). A Finite Element Implementation in Three Dimensions. In: A Finite Element Primer for Beginners. SpringerBriefs in Applied Sciences and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-09036-8_7

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  • DOI: https://doi.org/10.1007/978-3-319-09036-8_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-09035-1

  • Online ISBN: 978-3-319-09036-8

  • eBook Packages: EngineeringEngineering (R0)

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