English
Related papers

Related papers: Relationship between boundary integral equation an…

200 papers

Scattered data interpolation schemes using kriging and radial basis functions (RBFs) have the advantage of being meshless and dimensional independent, however, for the data sets having insufficient observations, RBFs have the advantage over…

Numerical Analysis · Mathematics 2018-06-12 Pankaj K Mishra , Sankar K Nath , Mrinal K Sen , Gregory E Fasshauer

In this work, we propose an adaptive radial basis function (RBF) approach for the efficient solution of multidimensional spatiotemporal integrodifferential equations. Our approach can automatically adjust the shape of RBFs and provide an…

Numerical Analysis · Mathematics 2026-04-08 Mingtao Xia , Qijing Shen

Low-rank approximations are popular methods to reduce the high computational cost of algorithms involving large-scale kernel matrices. The success of low-rank methods hinges on the matrix rank of the kernel matrix, and in practice, these…

Numerical Analysis · Computer Science 2020-10-22 Ruoxi Wang , Yingzhou Li , Eric Darve

Localized collocation methods based on radial basis functions (RBFs) for elliptic problems appear to be non-robust in the presence of Neumann boundary conditions. In this paper we overcome this issue by formulating the RBF-generated finite…

Numerical Analysis · Mathematics 2021-03-16 Igor Tominec , Elisabeth Larsson , Alfa Heryudono

In this paper, we present a spectral method based on Radial Basis Functions (RBFs) for numerically solving the fully nonlinear 1D Serre Green-Naghdi equations. The approximation uses an RBF discretization in space and finite differences in…

Fluid Dynamics · Physics 2014-07-17 Maurice S. Fabien

Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for big scattered datasets in $n-$dimensional space. It is a non-separable approximation, as it is…

Computational Engineering, Finance, and Science · Computer Science 2018-06-22 Zuzana Majdisova , Vaclav Skala

The paper introduces a new meshfree pseudospectral method based on Gaussian radial basis functions (RBFs) collocation to solve fractional Poisson equations. Hypergeometric functions are used to represent the fractional Laplacian of Gaussian…

Numerical Analysis · Mathematics 2024-01-01 Xiaochuan Tian , Yixuan Wu , Yanzhi Zhang

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…

Numerical Analysis · Mathematics 2017-05-23 Jingyang Guo , Jae-Hun Jung

This paper proposes a novel structure-aware matrix completion framework assisted by radial basis function (RBF) interpolation for near-field radio map construction in extremely large multiple-input multiple-output (XL-MIMO) systems. Unlike…

Signal Processing · Electrical Eng. & Systems 2025-11-11 Hao Sun , Xianghao Yu , Junting Chen

We present a new computational method by extending the Immersed Boundary (IB) method with a spectrally-accurate geometric model based on Radial Basis Function (RBF) interpolation of the Lagrangian structures. Our specific motivation is the…

Numerical Analysis · Mathematics 2015-05-27 Varun Shankar , Grady B. Wright , Robert M. Kirby , Aaron L. Fogelson

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 dimensions. Our approach introduces an adaptive mechanism by…

Numerical Analysis · Mathematics 2026-03-25 José Kuruc , David Levin , Pep Mulet , Juan Ruiz-Álvarez , Dionisio F. Yáñez

This contribution presents a new analysis of properties of the interpolation using Radial Bases Functions (RBF) related to large data sets interpolation. The RBF application is convenient method for scattered d-dimensional interpolation.…

Numerical Analysis · Mathematics 2017-08-01 Vaclav Skala

The radial basis function (RBF) approach is applied in predicting nuclear masses for 8 widely used nuclear mass models, ranging from macroscopic-microscopic to microscopic types. A significantly improved accuracy in computing nuclear masses…

Nuclear Theory · Physics 2013-09-03 Z. M. Niu , Z. L. Zhu , Y. F. Niu , B. H. Sun , T. H. Heng , J. Y. Guo

Quadrature formulas (QFs) based on radial basis functions (RBFs) have become an essential tool for multivariate numerical integration of scattered data. Although numerous works have been published on RBF-QFs, their stability theory can…

Numerical Analysis · Mathematics 2023-01-31 Jan Glaubitz , Jonah A. Reeger

In this paper we obtain approximated numerical solutions for the 2D Helmholtz equation using a radial basis function-generated finite difference scheme (RBF-FD), where weights are calculated by applying an oscillatory radial basis function…

Numerical Analysis · Mathematics 2019-03-05 Mauricio A. Londoño-Arboleda. , Hebert Montegranario

Runge--Kutta (RK) methods are widely used techniques for solving a class of initial value problems. In this article, we introduce an adaptive multiquadratic (MQ) radial basis function (RBF)-based method to develop enhanced explicit RK…

Numerical Analysis · Mathematics 2025-07-08 Rajesh Yadav , Deepak Kumar Yadav , Alpesh Kumar

The computation of global radial basis function (RBF) approximations requires the solution of a linear system which, depending on the choice of RBF parameters, may be ill-conditioned. We study the stability and accuracy of approximation…

Numerical Analysis · Mathematics 2022-11-24 Ben Adcock , Daan Huybrechs , Cécile Piret

One commonly finds in applications of smooth radial basis functions (RBFs) that scaling the kernels so they are `flat' leads to smaller discretization errors. However, the direct numerical approach for computing with flat RBFs (RBF-Direct)…

Numerical Analysis · Mathematics 2017-01-04 Grady B. Wright , Bengt Fornberg

Meshfree methods, including the reproducing kernel particle method (RKPM), have been widely used within the computational mechanics community to model physical phenomena in materials undergoing large deformations or extreme topology…

Numerical Analysis · Mathematics 2025-06-19 Jennifer E. Fromm , John A. Evans , J. S. Chen

This paper developed a systematic strategy establishing RBF on the wavelet analysis, which includes continuous and discrete RBF orthonormal wavelet transforms respectively in terms of singular fundamental solutions and nonsingular general…

Symbolic Computation · Computer Science 2007-05-23 W. Chen