Related papers: Weighted Essentially Non-Oscillatory Shepard metho…
Context. Several numerical problems require the interpolation of discrete data that present various types of discontinuities. The radiative transfer is a typical example of such a problem. This calls for high-order well-behaved techniques…
The weighted essentially non-oscillatory {technique} using a stencil of $2r$ points (WENO-$2r$) is an interpolatory method that consists in obtaining a higher approximation order from the non-linear combination of interpolants of $r+1$…
This work characterizes the structure of third and forth order WENO weights by deducing data bounded condition on third order polynomial approximations. Using these conditions, non-linear weights are defined for third and fourth order data…
In this work we present a new WENO b-spline based quasi-interpolation algorithm. The novelty of this construction resides in the application of the WENO weights to the b-spline functions, that are a partition of unity, instead to the…
The weighted essentially non-oscillatory (WENO) schemes are a popular class of high order accurate numerical methods for solving hyperbolic partial differential equations (PDEs). The computational cost of such schemes increases…
Accurate and efficient reconstruction techniques are essential in multiresolution analysis and image compression, particularly when the data are represented as cell averages. In this work, we present a non-separable progressive multivariate…
A modified Weighted Essentially Non-Oscillatory (WENO) reconstruction technique preventing accuracy loss near critical points (regardless of their order) of the underlying data is presented. This approach only uses local data from the…
ENO (Essentially Non-Oscillatory) and WENO (Weighted Essentially Non-Oscillatory) schemes are widely used high-order schemes for solving partial differential equations (PDEs), especially hyperbolic conservation laws with piecewise smooth…
In this paper, we propose a simple hybrid WENO scheme to increase computational efficiency and decrease numerical dissipation. Based on the characteristic-wise approach, the scheme switches the numerical flux of each characteristic…
In this paper, a third-order weighted essentially non-oscillatory (WENO) scheme is developed for hyperbolic conservation laws on unstructured quadrilateral and triangular meshes. As a starting point, a general stencil is selected for the…
The essentially non-oscillatory (ENO) method is an efficient high order numerical method for solving hyperbolic conservation laws designed to reduce the Gibbs oscillations, if existent, by adaptively choosing the local stencil for the…
Data remap between non-matching meshes is a critical step in multiphysics coupling using a partitioned approach. The data fields being transferred often have jumps in function values or derivatives. It is important but very challenging to…
Conventional WENO3 methods are known to be highly dissipative at lower resolutions, introducing significant errors in the pre-asymptotic regime. In this paper, we employ a rational neural network to accurately estimate the local smoothness…
A novel scheme, based on third-order Weighted Essentially Non-Oscillatory (WENO) reconstructions, is presented. It attains unconditionally optimal accuracy when the data is smooth enough, even in presence of critical points, and…
Classical high-order weighted essentially non-oscillatory (WENO) schemes are designed to achieve optimal convergence order for smooth solutions and to maintain non-oscillatory behaviors for discontinuities. However, their spectral…
The approximation of data is a fundamental challenge encountered in various fields, including computer-aided geometric design, the numerical solution of partial differential equations, or the design of curves and surfaces. Numerous methods…
A set of arbitrarily high-order WENO schemes for reconstructions on nonuniform grids is presented. These non-linear interpolation methods use simple smoothness indicators with a linear cost with respect to the order, making them easy to…
This paper introduces the Non-linear Partition of Unity Method, a novel technique integrating Radial Basis Function interpolation and Weighted Essentially Non-Oscillatory algorithms. It addresses challenges in high-accuracy approximations,…
We develop two new ideas for interpolation on $\mathbb{S}^2$. In this first part, we will introduce a simple interpolation method named \textit{Spherical Interpolation of orDER} $n$ (SIDER-$n$) that gives a $C^{n}$ interpolant given $n \geq…
The present article is concerned scattered data approximation for higher dimensional data sets which exhibit an anisotropic behavior in the different dimensions. Tailoring sparse polynomial interpolation to this specific situation, we…