@article {ipa|Algorithms for the implementation of adaptive isogeometric methods using hierarchical splines|2016, title = {Algorithms for the implementation of adaptive isogeometric methods using hierarchical splines}, year = {2016}, month = {July}, pages = {37 p.}, institution = {CNR-IMATI}, type = {Working paper}, chapter = {1}, address = {Pavia}, abstract = {

In this article we introduce all the ingredients to develop adaptive isogeometric methods based on hierarchical splines. In particular, we give precise definitions of local refinement and coarsening that, unlike previously existing methods, can be understood as the inverse of each other. We also define simple and intuitive data structures for the implementation of hierarchical splines, and algorithms for refinement and coarsening that take advantage of local information. We complete the paper with some simple numerical tests to show the performance of the data structures and algorithms, that have been implemented in the opensource Octave/Matlab code GeoPDEs.

}, keywords = {Local refinement}, url = {http://irs.imati.cnr.it/reports/algorithms-implementation-adaptive-isogeometric-methods-using-hierarchical-splines}, author = {E.M. Garau and R. V{\'a}zquez} } @article {ipa|On quasi-interpolation operators in spline spaces|2015, title = {On quasi-interpolation operators in spline spaces}, year = {2015}, month = {December}, pages = {16 p.}, institution = {CNR-IMATI}, type = {Working paper}, address = {Pavia}, abstract = {

We propose the construction of a class of L2 stable quasi-interpolation operators onto the space of splines on tensor-product meshes, in any space dimension. The estimate we propose is robust with respect to knot repetition and to knot "vicinity" (up to p+1 knots), so it applies to the most general scenario in which the B-spline functions are known to be well defined.

}, keywords = {Quasi-interpolation}, url = {http://irs.imati.cnr.it/reports/irs15-03}, author = {A. Buffa and E.M. Garau and C. Giannelli and G. Sangalli} }