Related papers: Non-linear WENO B-spline based approximation metho…
In this paper, we are concerned with the shallow water flow model over non-flat bottom topography by high-order schemes. Most of the numerical schemes in the literature are developed from the original mathematical model of the shallow water…
We present a generalized formulation for reweighted least squares approximations. The goal of this article is twofold: firstly, to prove that the solution of such problem can be expressed as a convex combination of certain interpolants when…
To extract the approximate solutions in the case of nonlinear fractional order differential equations with the homogeneous and nonhomogeneous boundary conditions, the weighted residual method is embedded here. We exploit three methods such…
We consider the weighted least squares spline approximation of a noisy dataset. By interpreting the weights as a probability distribution, we maximize the associated entropy subject to the constraint that the mean squared error is…
Higher order finite difference Weighted Essentially Non-Oscillatory (WENO) schemes have been constructed for conservation laws. For multidimensional problems, they offer high order accuracy at a fraction of the cost of a finite volume WENO…
The usual power function error estimates do not capture the true order of uniform accuracy for thin plate spline interpolation to smooth data functions in one variable. In this paper we propose a new type of power function and we show,…
This paper deals with the following important research question. Traditionally, the neural network employs non-linear activation functions concatenated with linear operators to approximate a given physical phenomenon. They "fill the space"…
We consider fitting a bivariate spline regression model to data using a weighted least-squares cost function, with weights that sum to one to form a discrete probability distribution. By applying the principle of maximum entropy, the weight…
In this paper, we intend to use a B-spline quasi-interpolation (BSQI) technique to develop higher order hybrid schemes for conservation laws. As a first step, we develop cubic and quintic B-spline quasi-interpolation based numerical methods…
Tensor B-spline methods are a high-performance alternative to solve partial differential equations (PDEs). This paper gives an overview on the principles of Tensor B-spline methodology, shows their use and analyzes their performance in…
This article introduces a functional method for lower-dimensional smooth representations in terms of time-varying dissimilarities. The method incorporates dissimilarity representation in multidimensional scaling and smoothness approach of…
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. One contribution is the derivation of high order…
We study local approximation properties in hierarchical spline spaces through a twofold approach. First, we design and analyze a robust adaptive refinement algorithm to construct locally graded meshes. Second, we establish rigorous…
We present a new rational approximation algorithm based on the empirical interpolation method for interpolating a family of parametrized functions to rational polynomials with invariant poles, leading to efficient numerical algorithms for…
Numerically obtaining the inverse of a function is a common task for many scientific problems, often solved using a Newton iteration method. Here we describe an alternative scheme, based on switching variables followed by spline…
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…
Higher order finite difference Weighted Essentially Non-Oscillatory (WENO) schemes for conservation laws are extremely popular because, for multidimensional problems, they offer high order accuracy at a fraction of the cost of finite volume…
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…
The paper is devoted to problem of spline approximation. A new method of nodes location for curves and surfaces computer construction by means of B-splines and results of simulink-modeling is presented. The advantages of this paper is that…
We present adaptive finite difference ENO/WENO methods by adopting infinitely smooth radial basis functions (RBFs). This is a direct extension of the non-polynomial finite volume ENO/WENO method proposed by authors in \cite{GuoJung} to the…