Related papers: Unstructured spline spaces for isogeometric analys…
The concept of trimming, embedding, or immersing geometries into a computational background mesh has gained considerable attention in recent years, particularly in isogeometric analysis (IGA). In this approach, the physical domain is…
The spline space $C_k^r(\Delta)$ attached to a subdivided domain $\Delta$ of $\R^{d} $ is the vector space of functions of class $C^{r}$ which are polynomials of degree $\le k$ on each piece of this subdivision. Classical splines on planar…
In this study, we investigate and compare formulations for computing shape derivatives in bi-material level-set optimization with precise modeling of the interface. The level-set function is parameterized using B-splines, whose coordinates…
This paper introduces a new mathematical and numerical framework for surface analysis derived from the general setting of elastic Riemannian metrics on shape spaces. Traditionally, those metrics are defined over the infinite dimensional…
Multivariate piecewise polynomial functions (or splines) on polyhedral complexes have been extensively studied over the past decades and find applications in diverse areas of applied mathematics including numerical analysis, approximation…
In this work, we propose a convenient framework for infinite-dimensional analysis (including both real and complex analysis in infinite dimensions), in which differentiation (in some weak sense) and integration operations can be easily…
Under consideration methods of constructing trigonometric interpolation splines of two variables on rectangular areas. These methods are easily generalized to the case of trigonometric interpolation splines of several variables on such…
In this paper, we overview one promising avenue of progress at the mathematical foundation of deep learning: the connection between deep networks and function approximation by affine splines (continuous piecewise linear functions in…
This paper investigates spaces equipped with a family of metric-like functions satisfying certain axioms. These functions provide a unified framework for defining topology, uniformity, and diffeology. The framework is based on a family of…
A rather complete investigation of anisotropic Bessel potential, Besov, and H\"older spaces on cylinders over (possibly) noncompact Riemannian manifolds with boundary is carried out. The geometry of the underlying manifold near its 'ends'…
Isogeometric analysis (IGA) enables exact representations of computational geometries and higher-order approximation of PDEs. In non-smooth domains, however, singularities near corners limit the effectiveness of IGA, since standard methods…
We present an approximately $C^1$-smooth multi-patch spline construction which can be used in isogeometric analysis (IGA). A key property of IGA is that it is simple to achieve high order smoothness within a single patch. To represent more…
Spinorial methods have proven to be a powerful tool to study geometric properties of spin manifolds. Our aim is to continue the spinorial study of manifolds that are not necessarily spin. We introduce and study the notion of $G$-invariance…
We introduce truncated Besov and Triebel--Lizorkin function spaces and investigate their main properties: embeddings, interpolation, duality, lifting, traces. These new scales allow us to improve several known results in functional analysis…
Spectral analysis of open surfaces is gaining momentum for studying surface morphology in engineering, computer graphics, and medical domains. This analysis is enabled using proper parameterization approaches on the target analysis domain.…
In this paper, we investigate $C^2$ super-smoothness of the full $C^1$ cubic spline space on a Powell-Sabin refined triangulation, for which a B-spline basis can be constructed. Blossoming is used to identify the $C^2$ smoothness conditions…
This paper presents a general framework for calculating the dimension of spline spaces over arbitrary rectilinear partitions using the smoothing cofactor method. The approach extends existing dimension theory for polynomial splines over…
One of the unspoken challenges of tractography is choosing the right parameters for a given dataset or bundle. In order to tackle this challenge, we explore the multi-dimensional parameter space of tractography using streamline-specific…
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…
The parameterization of open and closed anatomical surfaces is of fundamental importance in many biomedical applications. Spherical harmonics, a set of basis functions defined on the unit sphere, are widely used for anatomical shape…