6 papers
Algebraic Methods for Supersmooth Spline Spaces
Deepesh Toshniwal, Nelly Villamizar
Multivariate piecewise polynomial functions (or splines) on polyhedral complexes have been extensively studied over the past decades and find applications in diverse areas of appli…
A general class of smooth rational splines: Application to construction of exact ellipses and ellipsoids
Hendrik Speleers, Deepesh Toshniwal
In this paper, we describe a general class of smooth rational splines that enables, in particular, exact descriptions of ellipses and ellipsoids - some of the most important…
The divergence-conforming immersed boundary method: Application to vesicle and capsule dynamics
Hugo Casquero, Carles Bona-Casas, Deepesh Toshniwal +3
We extend the recently introduced divergence-conforming immersed boundary (DCIB) method [1] to fluid-structure interaction (FSI) problems involving closed co-dimension one solids.…
A Tchebycheffian extension of multi-degree B-splines: Algorithmic computation and properties
Rene R. Hiemstra, Thomas J. R. Hughes, Carla Manni +2
In this paper we present an efficient and robust approach to compute a normalized B-spline-like basis for spline spaces with pieces drawn from extended Tchebycheff spaces. The exte…
Counting the dimension of splines of mixed smoothness: A general recipe, and its application to meshes of arbitrary topologies
Deepesh Toshniwal, Michael DiPasquale
In this paper we study the dimension of bivariate polynomial splines of mixed smoothness on polygonal meshes. Here, "mixed smoothness" refers to the choice of different orders of s…
Dimension of polynomial splines of mixed smoothness on T-meshes
Deepesh Toshniwal, Nelly Villamizar
In this paper we study the dimension of splines of mixed smoothness on axis-aligned T-meshes. This is the setting when different orders of smoothness are required across the edges…