相关论文: Effective grading refinement for locally linearly …

Given a system of triangles in the plane $\mathbb{R}^2$ along with given data of function and gradient values at the vertices, we describe the general pattern of local linear methods invoving only four smooth standard shape functions which…

We study the recovery of functions in real spline spaces from unsigned sampled values. We consider two types of recovery. The one is to recover functions locally from finitely many unsigned samples. And the other is to recover functions on…

We analyze the space of bivariate functions that are piecewise polynomial of bi-degree \textless{}= (m, m') and of smoothness r along the interior edges of a planar T-mesh. We give new combinatorial lower and upper bounds for the dimension…

Rescaled spike and slab models are a new Bayesian variable selection method for linear regression models. In high dimensional orthogonal settings such models have been shown to possess optimal model selection properties. We review…

This paper concerns with iterative schemes for the perfect reconstruction of functions belonging to multiresolution spaces on bounded manifolds from nonuniform sampling. The schemes have optimal complexity in the sense that the…

Splines can be constructed by convolving the indicator function of a cell whose shifts tessellate $\R^k$. This paper presents simple, non-algebraic criteria that imply that, for regular shift-invariant tessellations, only a small subset of…

We present a detailed numerical study on structure and local magnetic properties of $\langle 100 \rangle$ symmetric tilt grain boundaries in bcc-iron. Particular attention is paid to connection between type of grain boundary relaxation and…

Surface reconstruction with preservation of geometric features is a challenging computer vision task. Despite significant progress in implicit shape reconstruction, state-of-the-art mesh extraction methods often produce aliased,…

Convergence failure and slow convergence rate are among the biggest challenges with solving the system of non-linear equations numerically. While using strictly small time steps sizes and unconditionally stable fully implicit scheme…

State-of-the-art language models can exhibit impressive reasoning refinement capabilities on math, science or coding tasks. However, recent work demonstrates that even the best models struggle to identify \textit{when and where to refine}…

Dual pseudo splines constitute a new class of refinable functions with B-splines as special examples, which was introduced in \cite{DHSS}. In this paper, we shall construct Riesz wavelet associated with dual pseudo splines. Furthermore, we…

A new concept is introduced for the adaptive finite element discretization of partial differential equations that have a sparsely representable solution. Motivated by recent work on compressed sensing, a recursive mesh refinement procedure…

Mesh optimization procedures are generally a combination of node smoothing and discrete operations which affect a small number of elements to improve the quality of the overall mesh. These procedures are useful as a post-processing step in…

This paper demonstrates how an efficient representation of the planned path using B-splines, and a construction procedure that takes advantage of the neural network's inductive bias, speed up both the inference and training of a DNN-based…

This paper describes a node relocation algorithm based on nonlinear optimization which delivers excellent results for both unstructured and structured plane triangle meshes over convex as well as non-convex domains with high curvature. The…

Adaptive isogeometric methods for the solution of partial differential equations rely on the construction of locally refinable spline spaces. A simple and efficient way to obtain these spaces is to apply the multi-level construction of…

We present the design and implementation details of a geometric multigrid method on adaptively refined meshes for massively parallel computations. The method uses local smoothing on the refined part of the mesh. Partitioning is achieved by…

This paper addresses the challenge of grading visual features in lumbar spine MRI using Deep Learning. Such a method is essential for the automatic quantification of structural changes in the spine, which is valuable for understanding low…

We present a general variational framework for the training of freeform nonlinearities in layered computational architectures subject to some slope constraints. The regularization that we add to the traditional training loss penalizes the…

In this paper, we address the problem of constructing $C^2$ cubic spline functions on a given arbitrary triangulation $\mathcal{T}$. To this end, we endow every triangle of $\mathcal{T}$ with a Wang-Shi macro-structure. The $C^2$ cubic…