@article {irs17-01, title = {BPX preconditioners for isogeometric analysis using analysis-suitable T-splines}, number = {17-01}, year = {2017}, month = {January}, pages = {32 p.}, publisher = {CNR-IMATI}, type = {Working paper}, address = {Pavia}, abstract = {

We propose and analyze optimal additive multilevel solvers for isogeometric discretizations of scalar elliptic problems for locally refined T-meshes. Applying the refinement strategy in Morgenstern and Peterseim, Comput. Aided Geom. Design, 34 (2015), we can guarantee that the obtained T-meshes are p-admissible, which implies that the associated T-splines are analysis suitable. Taking advantage of the multilevel structure of p-admissible T-meshes, we develop a BPX preconditioner on the basis of local smoothing only for the functions affected by a newly added edge by bisection, and prove that our method has optimal complexity. Several numerical experiments confirm our theoretical result and also show the practical performance of the proposed preconditioner.

}, keywords = {T-splines}, doi = {https://doi.org/10.1093/imanum/dry032}, url = {http://irs.imati.cnr.it/reports/irs17-01}, author = {D. Cho and R. V{\'a}zquez} } @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|A new design for the implementation of isogeometric analysis in Octave and Matlab: GeoPDEs 3.0|2016, title = {A new design for the implementation of isogeometric analysis in Octave and Matlab: GeoPDEs 3.0}, year = {2016}, month = {April}, pages = {44 p.}, institution = {IMATI-CNR}, type = {Working paper}, address = {Pavia}, abstract = {

GeoPDEs (http://rafavzqz.github.io/geopdes)\  is an Octave/Matlab package for the solution of partial differential equations with isogeometric analysis, first released in 2010. In this work we present in detail the new design of the package, based on the use of Octave and Matlab classes. Compared to previous versions the new design is much clearer, and it is also more efficient in terms of memory consumption and computational time.

}, keywords = {Structure-preserving discretizations}, url = {http://irs.imati.cnr.it/reports/irs16-02}, author = {R. V{\'a}zquez} }