Isogeometric collocation methods with generalized B-splines

We introduce isogeometric collocation methods based on generalized B-splines and we analyze their performance through numerical examples for univariate and multivariate scalar- and vector-valued problems. In particular, advection-diffusion and linear elasticity model problems are addressed. The resulting method combines the favorable properties of isogeometric collocation and the geometrical and analytical problem-oriented advantages of generalized B-splines.