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

Paweł Piotr Lipski, Maciej Paszyński

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


finite element method, isogeometric analysis, parallel computing, h-adaptivity, B-splines

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References


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

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