1 citations · 1 across the 19 of their papers we have counts for
20 papers
Data-dependent Compact Multinode Shepard Method
Francesco Dell'Accio, Filomena Di Tommaso, Francesco Larosa +2
We introduce a data-dependent compact multinode Shepard method for the approximation of scattered multivariate data. The proposed approach extends the compact multinode Shepard ope…
Adaptive Non-Linear Partition of Unity Methods for Scattered Data Interpolation with Discontinuities
Adeeba Haider, Roberto Cavoretto, Juan Ruiz-Álvarez +1
Scattered data approximation with discontinuities is challenging due to the Gibbs phenomenon, which significantly reduces accuracy near interfaces. The recently introduced Non-Line…
Data dependent Shepard approximation through and adaptive modification of the shape parameter
José Kuruc, Juan Ruiz-Álvarez, Bo Wang +1
In this article, we introduce a novel data-dependent Shepard interpolation method inspired by the adaptive strategies proposed in [2]. In this case, as Shepard interpolation does n…
Data-dependent approximation through RBF
José Kuruc, David Levin, Pep Mulet +2
In this article we present a modification of classical Radial Basis Function (RBF) interpolation techniques aimed at reducing oscillations near discontinuities in one and two dimen…
A Cell-Average Non-Separable Progressive Multivariate WENO Method for Image Processing Applications
Inmaculada Garcés, Pep Mulet, Juan Ruiz-Álvarez +2
Accurate and efficient reconstruction techniques are essential in multiresolution analysis and image compression, particularly when the data are represented as cell averages. In th…
Multivariate Data-dependent Partition of Unity based on Moving Least Squares method
Inmaculada Garcés, Juan Ruiz-Álvarez, Dionisio F. Yáñez
Data approximation is essential in fields such as geometric design, numerical PDEs, and curve modeling. Moving Least Squares (MLS) is a widely used method for data fitting; however…
A general correction for numerical integration rules over piece-wise continuous functions
Shipra Mahata, Samala Rathan, Juan Ruiz-Álvarez +1
This article presents a novel approach to enhance the accuracy of classical quadrature rules by incorporating correction terms. The proposed method is particularly effective when t…
Integrating Moving Least Squares with non-linear WENO method: A novel Partition of Unity approach in 1D
Inmaculada Garcés, José M. Ramón, Juan Ruiz-Álvarez +1
The approximation of data is a fundamental challenge encountered in various fields, including computer-aided geometric design, the numerical solution of partial differential equati…
Non-linear Partition of Unity method
José Manuel Ramón, Juan Ruiz-Alvarez, Dionisio F. Yáñez
This paper introduces the Non-linear Partition of Unity Method, a novel technique integrating Radial Basis Function interpolation and Weighted Essentially Non-Oscillatory algorithm…
Data dependent Moving Least Squares
David Levin, José M. Ramón, Juan Ruiz-Alvarez +1
In this paper, we address a data dependent modification of the moving least squares (MLS) problem. We propose a novel approach by replacing the traditional weight functions with ne…
Weighted Essentially Non-Oscillatory Shepard method
David Levin, José M. Ramón, Juan Ruiz-Alvarez +1
Shepard method is a fast algorithm that has been classically used to interpolate scattered data in several dimensions. This is an important and well-known technique in numerical an…
A non-separable progressive multivariate WENO- point value
Pep Mulet, Juan Ruiz-Alvarez, Chi-Wang Shu +1
The weighted essentially non-oscillatory {technique} using a stencil of points (WENO-) is an interpolatory method that consists in obtaining a higher approximation order f…
Non-linear WENO B-spline based approximation method
Sergio Amat, David Levin, Juan Ruiz-Álvarez +1
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 fun…
Numerical integration rules with improved accuracy close to singularities
Sergio Amat, Zhilin Li, Juan Ruiz-Alvarez +2
Sometimes it is necessary to obtain a numerical integration using only discretised data. In some cases, the data contains singularities which position is known but does not coincid…
High order two-grid finite difference methods for interface and internal layer problems
Zhilin Li, Kejia Pan, Juan Ruiz
Second order accurate Cartesian grid methods have been well developed for interface problems in the literature. However, it is challenging to develop third or higher order accurate…
Global and explicit approximation of piecewise smooth 2D functions from cell-average data
Sergio Amat, David Levin, Juan Ruiz-Alvarez +1
Given cell-average data values of a piecewise smooth bivariate function within a domain , we look for a piecewise adaptive approximation to . We are interested in an expl…
Explicit multivariate approximations from cell-average data
Sergio Amat, David Levin, Juan Ruiz-Alvarez +1
Given gridded cell-average data of a smooth multivariate function, we present a constructive explicit procedure for generating a high-order global approximation of the function. On…
Convergence study of IB methods for Stokes equations with no-slip boundary conditions
Zhilin Li, Kejia Pan, Juan Ruiz-Álvarez
Peskin's Immersed Boundary (IB) model and method are among one of the most important modeling tools and numerical methods. The IB method has been known to be first order accurate i…
Corrected approximation strategy for piecewise smooth bivariate functions
Sergio Amat, David Levin, Juan Ruiz-Álvarez
Given values of a piecewise smooth function on a square grid within a domain , we look for a piecewise adaptive approximation to . Standard approximation techniques achie…
On a regularization-correction approach for the approximation of piecewise smooth functions
Sergio Amat, David Levin, Juan Ruiz-Álvarez
Linear approximation approaches suffer from Gibbs oscillations when approximating functions with singularities. ENO-SR resolution is a local approach avoiding oscillations and with…