Related papers: Manifold-based isogeometric analysis basis functio…

In this paper, we propose a spectral method for deriving functions that are jointly smooth on multiple observed manifolds. This allows us to register measurements of the same phenomenon by heterogeneous sensors, and to reject…

Closed (and simply-connected) manifolds whose dimensions are larger than 4 are central geometric objects in classical algebraic topology and differential topology. They have been classified via algebraic and abstract objects. On the other…

We analyze the space of geometrically continuous piecewise polynomial functions or splines for quadrangular and triangular patches with arbitrary topology and general rational transition maps. To define these spaces of G 1 spline functions,…

We consider the regression problem of estimating functions on $\mathbb{R}^D$ but supported on a $d$-dimensional manifold $ \mathcal{M} \subset \mathbb{R}^D $ with $ d \ll D $. Drawing ideas from multi-resolution analysis and nonlinear…

This monograph presents a geometric modeling method nonlinear dynamical systems from experimental data . basis method is a qualitative approach to the analysis of linear models and construction of the symmetry groups of attractors of…

Starting from the axiomatic description of meromorphic functions with prescribed analytic properties, we introduce the cosimplicial cohomology of restricted meromorphic functions defined on foliations of smooth complex manifolds. Spaces for…

Establishing dense correspondence across 3D shapes is crucial for fundamental downstream tasks, including texture transfer, shape interpolation, and robotic manipulation. However, learning these mappings without manual supervision remains a…

Constructing Morse functions and their higher dimensional versions or fold maps is fundamental, important and challenging in investigating the topologies and the differentiable structures of differentiable manifolds via Morse functions,…

Many coupled problems in engineering and science can be described by elliptic partial differential equations on adjacent domains, where the coupling can be considered either as a thin equidimensional overlap between the model domains, or as…

This work develops a computational framework that combines physics-informed neural networks with multi-patch isogeometric analysis to solve partial differential equations on complex computer-aided design geometries. The method utilizes…

We introduce a new regression framework designed to deal with large-scale, complex data that lies around a low-dimensional manifold with noises. Our approach first constructs a graph representation, referred to as the skeleton, to capture…

Manifold learning techniques have become increasingly valuable as data continues to grow in size. By discovering a lower-dimensional representation (embedding) of the structure of a dataset, manifold learning algorithms can substantially…

Isogeometric analysis (IgA) uses the same class of basis functions for both, representing the geometry of the computational domain and approximating the solution. In practical applications, geometrical patches are used in order to get…

Human brain connectome studies aim at extracting and analyzing relevant features associated to pathologies of interest. Usually this consists in modeling the brain connectome as a graph and in using graph metrics as features. A fine brain…

Mesh adaptivity is a technique to provide detail in numerical solutions without the need to refine the mesh over the whole domain. Mesh adaptivity in isogeometric analysis can be driven by Truncated Hierarchical B-splines (THB-splines)…

High-dimensional datasets often exhibit low-dimensional geometric structures, as suggested by the manifold hypothesis, which implies that data lie on a smooth manifold embedded in a higher-dimensional ambient space. While this insight…

We propose a novel 3D shape correspondence method based on the iterative alignment of so-called smooth shells. Smooth shells define a series of coarse-to-fine shape approximations designed to work well with multiscale algorithms. The main…

This paper deals with a special class of parametrizations for Isogeometric Analysis (IGA). The so-called scaled boundary parametrizations are easy to construct and particularly attractive if only a boundary description of the computational…

This article presents families of 7-dimensional closed and simply-connected manifolds and fold maps on them such that squares of 2nd integral cohomology classes may not be divisible by 2. Fold maps are higher dimensional versions of Morse…

Isogeometric analysis (IGA) has emerged as a promising approach in the field of structural optimization, benefiting from the seamless integration between the computer-aided design (CAD) geometry and the analysis model by employing…