Related papers: $C^s$-smooth isogeometric spline spaces over plana…
In this paper hierarchical analysis-suitable T-splines (HASTS) are developed. The resulting spaces are a superset of both analysis-suitable T-splines and hierarchical B-splines. The additional flexibility provided by the hierarchy of…
Continuous spline functions are defined as piecewise polynomials on the faces of a polyhedral complex that agree on the intersections of two faces. Splines are used in approximation theory and numerical analysis, with applications in data…
Estimation of the covariance structure of spatial processes is of fundamental importance in spatial statistics. In the literature, several non-parametric and semi-parametric methods have been developed to estimate the covariance structure…
Subdivision surfaces provide an elegant isogeometric analysis framework for geometric design and analysis of partial differential equations defined on surfaces. They are already a standard in high-end computer animation and graphics and are…
We outline the construction of compatible B-splines on 3D surfaces that satisfy the continuity requirements for electromagnetic scattering analysis with the boundary element method (method of moments). Our approach makes use of Non-Uniform…
The construction of $C^m$ conforming finite elements on simplicial meshes has recently advanced through the groundbreaking work of Hu, Lin, and Wu (Found. Comput. Math. 24, 2024). Their framework characterizes smoothness via moments of…
This paper introduces the concept of dimensional stability for spline spaces over T-meshes, providing the first mathematical definition and a preliminary classification framework. We define dimensional stability as an invariant within the…
Imagine a swarm of terrestrial robots that can explore an environment, and, upon completion of this task, reconfigure into a spherical ball and roll out. This dimensional change alters the dynamics of locomotion and can assist them to…
This work presents numerical techniques to enforce continuity constraints on multi-patch surfaces for three distinct problem classes. The first involves structural analysis of thin shells that are described by general Kirchhoff-Love…
The present paper is concerned with new Besov-type space of variable smoothness. Nonlinear spline-approximation approach is used to give atomic decomposition of such space. Characterization of the trace space on hyperplane is also obtained.
We consider dual-primal isogeometric tearing and interconnection (IETI-DP) solvers for multi-patch geometries in Isogeometric Analysis. Recently, the authors have published a convergence analysis for those solvers that is explicit in both…
In this work, we compare the nodal and isogeometric spatial discretization schemes for the nonlinear formulation of shear- and torsion-free rods introduced in [1]. We investigate the resulting discrete solution space, the accuracy, and the…
In this paper, a method is proposed to solve the problem of monotone smoothing splines using general linear systems. This problem, also called monotone control theoretic splines, has been solved only when the curve generator is modeled by…
Penalty methods have proven to be particularly effective for achieving the required $C^1$-continuity in the context of multi-patch isogeometric Kirchhoff-Love shells. Due to their conceptual simplicity, these algorithms are readily…
We introduce a family of variational functionals for spinor fields on a compact Riemann surface $M$ that can be used to find close-to-conformal immersions of $M$ into $\mathbb{R}^3$ in a prescribed regular homotopy class. Numerical…
We propose a novel method to determine the dissimilarity between subjects for functional data clustering. Spline smoothing or interpolation is common to deal with data of such type. Instead of estimating the best-representing curve for each…
We provide a comprehensive study of interrelations between different measures of smoothness of functions on various domains and smoothness properties of approximation processes. Two general approaches to this problem have been developed:…
This paper considers the development of spatially adaptive smoothing splines for the estimation of a regression function with non-homogeneous smoothness across the domain. Two challenging issues that arise in this context are the evaluation…
In this survey article we provide an introduction to submanifold geometry in symmetric spaces of noncompact type. We focus on the construction of examples and the classification problems of homogeneous and isoparametric hypersurfaces, polar…
We consider spline functions over simplicial meshes in $\RR^n$. We assume that the spline pieces join together with some finite order of smoothness but the pieces themselves are infinitely smooth. Such splines can have extra orders of…