相关论文: Globally structured 3D Analysis-suitable T-splines…

Multi-degree splines are smooth piecewise-polynomial functions where the pieces can have different degrees. We describe a simple algorithmic construction of a set of basis functions for the space of multi-degree splines, with similar…

We propose a novel architecture for graph-based dependency parsing that explicitly constructs vectors, from which both arcs and labels are scored. Our method addresses key limitations of the standard two-pipeline approach by unifying arc…

This work presents a multilevel approach to large--scale topology optimization accounting for linearized buckling criteria. The method relies on the use of preconditioned iterative solvers for all the systems involved in the linear buckling…

Self-shaping of curved structures, especially those involving flexible thin layers, has attracted increasing attention because of their broad potential applications in e.g. nanoelectromechanical/micro-electromechanical systems (NEMS/MEMS),…

This paper is devoted to second-order variational analysis of a rather broad class of extended-real-valued piecewise liner functions and their applications to various issues of optimization and stability. Based on our recent explicit…

Isogeometric analysis is a recently developed framework based on finite element analysis, where the simple building blocks in geometry and solution space are replaced by more complex and geometrically-oriented compounds. Box splines are an…

Delineation of curvilinear structures is an important problem in Computer Vision with multiple practical applications. With the advent of Deep Learning, many current approaches on automatic delineation have focused on finding more powerful…

In this paper we introduce a new class of diffeomorphic smoothers based on general spline smoothing techniques and on the use of some tools that have been recently developed in the context of image warping to compute smooth diffeomorphisms.…

Relu Fully Connected Networks are ubiquitous but uninterpretable because they fit piecewise linear functions emerging from multi-layered structures and complex interactions of model weights. This paper takes a novel approach to piecewise…

The novel Locally Refined B-spline (LR B-spline) surface format is suited for representing terrain and seabed data in a compact way. It provides an alternative to the well know raster and triangulated surface representations. An LR B-spline…

This study explores the explainability capabilities of large language models (LLMs), when employed to autonomously generate machine learning (ML) solutions. We examine two classification tasks: (i) a binary classification problem focused on…

We present weighted quadrature for hierarchical B-splines to address the fast formation of system matrices arising from adaptive isogeometric Galerkin methods with suitably graded hierarchical meshes. By exploiting a local tensor-product…

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 contribution introduces the idea of refinement patterns for the generation of optimal meshes in the context of the Finite Element Method. The main idea is to generate a library of possible patterns on which elements can be refined and…

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 smoothness across different edges of the mesh. To study the…

We introduce a family of boundary conditions and point constraints for conformal immersions that increase the controllability of surfaces defined as minimizers of conformal variational problems. Our free boundary conditions fix the metric…

The rigorous convergence analysis of adaptive finite element methods for regularized variational models of quasi-static brittle fracture in strain-limiting elastic solids is presented. This work introduces two novel adaptive mesh refinement…

We explore extended B-splines as a stable basis for isogeometric analysis with trimmed parameter spaces. The stabilization is accomplished by an appropriate substitution of B-splines that may lead to ill-conditioned system matrices. The…

Unsupervised and supervised learning methods conventionally use kernels to capture nonlinearities inherent in data structure. However experts have to ensure their proposed nonlinearity maximizes variability and capture inherent diversity of…

Given a spline space spanned by Truncated Hierarchical B-splines (THB), it is always possible to construct a spline space spanned by Locally Refined B-splines (LRB) that contains the THB-space. Starting from configurations where the two…