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

This paper deals with an adaptive finite element method originally developedby Prof. Leszek Demkowicz for hierarchical basis functions. In this paper, weinvestigate the extension of the adaptive algorithm for isogeometric analysisperformed with B-spline basis functions. We restrict ourselves to h-adaptivity,since the polynomial order of approximation must be fixed in the isogeometriccase. The classical variant of the adaptive FEM algorithm, as delivered by thegroup of Prof. Demkowicz, is based on a two-grid paradigm, with coarse andfine grids (the latter utilized as a reference solution). The problem is solved independentlyover a coarse mesh and a fine mesh. The fine-mesh solution is thenutilized as a reference to estimate the relative error of the coarse-mesh solutionand to decide which elements to refine. Prof. Demkowicz uses hierarchicalbasis functions, which (though locally providing C p−1 continuity) ensure onlyC 0 on the interfaces between elements. The CUDA C library described in thispaper switches the basis to B-spline functions and proposes a one-dimensionalisogeometric version of the h-adaptive FEM algorithm to achieve global C p−1continuity of the solution