### One-dimensional fully automatic h-adaptive isogeometric finite element method package

#### Abstract

This paper deals with an adaptive finite element method originally developed

by Prof. Leszek Demkowicz for hierarchical basis functions. In this paper, we

investigate the extension of the adaptive algorithm for isogeometric analysis

performed with B-spline basis functions. We restrict ourselves to h-adaptivity,

since the polynomial order of approximation must be fixed in the isogeometric

case. The classical variant of the adaptive FEM algorithm, as delivered by the

group of Prof. Demkowicz, is based on a two-grid paradigm, with coarse and

fine grids (the latter utilized as a reference solution). The problem is solved independently

over a coarse mesh and a fine mesh. The fine-mesh solution is then

utilized as a reference to estimate the relative error of the coarse-mesh solution

and to decide which elements to refine. Prof. Demkowicz uses hierarchical

basis functions, which (though locally providing C p−1 continuity) ensure only

C 0 on the interfaces between elements. The CUDA C library described in this

paper switches the basis to B-spline functions and proposes a one-dimensional

isogeometric version of the h-adaptive FEM algorithm to achieve global C p−1

continuity of the solution.

#### Keywords

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PDF#### References

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DOI: http://dx.doi.org/10.7494/csci.2016.17.4.439

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