We derive new trace inequalities for NURBS-mapped domains. In addition to Sobolev-type inequalities, we derive discrete trace inequalities for use in NURBS-based isogeometric analysis. All dependencies on shape, size, polynomial order, and the NURBS weighting function are precisely specified in our analysis, and explicit values are provided for all bounding constants appearing in our estimates....

In usual boundary elements methods, the mixed Dirichlet-Neumann problem in a plane polygonal domain leads to difficulties because of the transition of spaces in which the problem is well posed. We build collocation methods based on a mixed single and double layer potential. This indirect method is constructed in such a way that strong ellipticity is obtained in high order spaces of Sobolev type...

A geometrically exact membrane formulation is presented that is based on curvilinear coordinates and isogeometric finite elements, and is suitable for both solid and liquid membranes. The curvilinear coordinate system is used to describe both the theory and the finite element equations of the membrane. In the latter case this avoids the use of local cartesian coordinates at the element level. C...

We derive a new “convolution spline” approximation method for convolution Volterra integral equations. This shares some properties of convolution quadrature, but instead of being based on an underlying ODE solver is explicitly constructed in terms of basis functions which have compact support. At time step tn = nh > 0, the solution is approximated in a “backward time” manner in terms of basis f...

The determination of the approximation power of spaces of multivariate splines with the aid of quasiinterpolants is reviewed. In the process, a streamlined description of the existing quasiinterpolant theory is given. 1. Approximation power of splines I begin with a brief review of the approximation power of univariate splines since the techniques for its investigation are also those with which...

We propose a novel reconstruction method using a spline-based image model in both spatial and temporal dimensions that takes the advantage of the precise timing of each k-space sample to reconstruct image series at high time frames, independently from the original sampling rate of data and avoiding the temporal blurring that can affect other reconstruction methods like sliding window. While MRI...

The so-called motorcycle graph has been employed in recent years for various purposes the context of structured and aligned block decomposition 2D shapes 2-manifold surfaces. Applications are fields surface parametrization, spline space construction, semi-structured quad mesh generation, or geometry data compression. We describe a generalization this concept to three-dimensional volumetric sett...