Isogeometric collocation using analysis-suitable T-splines of arbitrary degree

This paper deals with the use of analysis-suitable T-splines of arbitrary degree in combination with isogeometric collocation methods for the solution of second- and fourth-order boundary-value problems. In fact, analysis-suitable T-splines appear to be a particularly efficient locally refinable basis for isogeometric collocation, able to conserve the cost of only one point evaluation per degree of freedom typical of standard NURBS-based isogeometric collocation. Furthermore, T-splines allow to easily create highly non-uniform meshes without introducing elements with high aspect ratios; this makes it possible to avoid the numerical instabilities that may arise in the case of problems characterized by reduced regularity when Neumann boundary conditions are imposed in strong form and elements with high aspect ratio are used. The local refinement properties of T-splines can be also successfully exploited to approximate problems where point loads are applied. Finally, several numerical tests are herein presented in order to confirm all the above-mentioned features, as well as the good overall convergence properties of the combination of isogeometric collocation and analysis-suitable T-splines.