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We study the spectral properties of stiffnessmatrices that arise in the context\ud of isogeometric analysis for the numerical solution of classical second order elliptic\ud problems. Motivated by the applicative interest in the fast solution of the related linear\ud systems, we are looking for a spectral characterization of the involved matrices. In\ud particular, we investigate non-singularity, conditioning (extremal behavior), spectral\ud distribution in the Weyl sense, as well as clustering of the eigenvalues to a certain\ud (compact) subset of C. All the analysis is related to the notion of symbol in the\ud Toeplitz setting and is carried out both for the cases of 1D and 2D problems

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Quadratic Powell-Sabin splines and their rational extension, the socalled NURPS surfaces, are an interesting alternative for classical tensor-product NURBS in the context of isogeometric analysis, because they allow the use of local refinements while retaining a Bspline like representation and exact description of conic sections. In this paper we present a simple and effective strategy to convert a given planar geometry defined by a quadratic NURBS representation into a NURPS representation, suitable for the analysis.Keywords : Powell-Sabin splines, NURBS, NURPS, isogeometric analysis. AbstractQuadratic Powell-Sabin splines and their rational extension, the so-called NURPS surfaces, are an interesting alternative for classical tensor-product NURBS in the context of isogeometric analysis, because they allow the use of local refinements while retaining a B-spline like representation and exact description of conic sections. In this paper we present a simple and effective strategy to convert a given planar geometry defined by a quadratic NURBS representation into a NURPS representation, suitable for the analysis.

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