Efficient r-adaptive isogeometric analysis with Winslow’s mapping and monitor function approach

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Abstract

Motivated by the moving mesh method in conventional finite element analysis, in this paper, we propose an r-adaptive isogeometric analysis framework by Winslow’s mapping and monitor function approach. We construct a new monitor function based on the absolute curvature metric of the isogeometric solution surface. In the proposed r-adaptive framework, the redistribution of the inner control points is performed to increase the density of control points in the regions where curvature based or error based monitor functions are maximum. The new locations of the inner control points are obtained by solving governing PDEs using isogeometric collocation method which is more efficient in solving large-scale problems. By employing Winslow’s mapping we ensure that the generated r-adaptive parameterization is valid for isogeometric analysis and can be used as optimal initial grid for subsequent h-refinements. Multiple two-dimensional heat conduction examples are solved which confirm the effectiveness of the proposed method.

Keywords

Isogeometric analysis
r-adaptive method
Winslow’s mapping
Monitor function
Heat conduction

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