相关论文: Polynomial preserving recovery for PHT-splines

We introduce adaptive particle refinement for compressible smoothed particle hydrodynamics (SPH). SPH calculations have the natural advantage that resolution follows mass, but this is not always optimal. Our implementation allows the user…

Recently, deep learning methods have gained remarkable achievements in the field of image restoration for remote sensing (RS). However, most existing RS image restoration methods focus mainly on conventional first-order degradation models,…

We use Deep Operator Networks (DeepONets) to perform super-resolution reconstruction of the solutions of two types of partial differential equations and compare the model predictions with the results obtained using conventional…

In this paper we provide a priori error estimates in standard Sobolev (semi-)norms for approximation in spline spaces of maximal smoothness on arbitrary grids. The error estimates are expressed in terms of a power of the maximal grid…

In this work, we introduce new families of nonconforming approximation methods for reconstructing functions on general polygonal meshes. These methods are defined using degrees of freedom based on weighted moments of orthogonal polynomials…

We show that the sparse polynomial interpolation problem reduces to a discrete super-resolution problem on the $n$-dimensional torus. Therefore the semidefinite programming approach initiated by Cand\`es \\& Fernandez-Granda…

Structures matter in single image super resolution (SISR). Recent studies benefiting from generative adversarial network (GAN) have promoted the development of SISR by recovering photo-realistic images. However, there are always undesired…

We propose an adaptive mesh refinement strategy for immersed isogeometric analysis, with application to steady heat conduction and viscous flow problems. The proposed strategy is based on residual-based error estimation, which has been…

In this paper, we formally investigate two mathematical aspects of Hermite splines which translate to features that are relevant to their practical applications. We first demonstrate that Hermite splines are maximally localized in the sense…

This paper proposes an Adaptive Isogeometric Topology Optimization framework for shell structures based on PHT-splines (PHT-AITO). In this framework, the design domain, displacement, and density are represented by PHT-splines. Leveraging…

We introduce a family of piecewise-exponential functions that have the Hermite interpolation property. Our design is motivated by the search for an effective scheme for the joint interpolation of points and associated tangents on a curve…

A posteriori estimates give bounds on the error between the unknown solution of a partial differential equation and its numerical approximation. We present here the methodology based on H1-conforming potential and H(div)-conforming…

Multivariate global polynomial approximations - such as polynomial chaos or stochastic collocation methods - are now in widespread use for sensitivity analysis and uncertainty quantification. The pseudospectral variety of these methods uses…

In this paper we describe an adaptive refinement strategy for LR B-splines. The presented strategy ensures, at each iteration, local linear independence of the obtained set of LR B-splines. This property is then exploited in two…

We propose a new method of adaptive piecewise approximation based on Sinc points for ordinary differential equations. The adaptive method is a piecewise collocation method which utilizes Poly-Sinc interpolation to reach a preset level of…

The idea of compressed sensing is to exploit representations in suitable (overcomplete) dictionaries that allow to recover signals far beyond the Nyquist rate provided that they admit a sparse representation in the respective dictionary.…

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…

In this paper, we propose a new trigonometric interpolation algorithm and establish relevant convergent properties. The method adjusts an existing trigonometric interpolation algorithm such that it can better leverage Fast Fourier Transform…

Recovering the missing regions of an image is a task that is called image inpainting. Depending on the shape of missing areas, different methods are presented in the literature. One of the challenges of this problem is extracting features…

This paper develops a unified theory of natural superconvergence points for polynomial spline approximations to second-order elliptic problems. Beginning with the one-dimensional case, we establish that when a point $x_0$ is a local…