[PDF][PDF] Multiquadric radial basis function approximation methods for the numerical solution of partial differential equations

SA Sarra, EJ Kansa - Advances in Computational Mechanics, 2009‏ - scottsarra.org
Radial Basis Function (RBF) methods have become the primary tool for interpolating
multidimensional scattered data. RBF methods also have become important tools for solving …

Model-based calibration for magnetic manipulation

AJ Petruska, J Edelmann… - IEEE Transactions on …, 2017‏ - ieeexplore.ieee.org
Model-based calibration of a magnetic workspace not only provides a smooth
representation of the field and its gradient matrix, but also uses physical constraints to …

On radial basis functions

M Buhmann, J Jäger - 2019‏ - publications.mfo.de
Many sciences and other areas of research and applications from engineering to economics
require the approximation of functions that depend on many variables. This can be for a …

Divergence-free kernel methods for approximating the Stokes problem

H Wendland - SIAM Journal on Numerical Analysis, 2009‏ - SIAM
We develop a new discretization scheme for the Stokes equations using analytically
divergence-free approximation spaces. Our scheme is based upon a meshfree method …

A numerical solution of nonlinear parabolic-type Volterra partial integro-differential equations using radial basis functions

Z Avazzadeh, ZB Rizi, FMM Ghaini… - Engineering analysis with …, 2012‏ - Elsevier
In this paper, an effective numerical method for solving nonlinear Volterra partial integro-
differential equations is proposed. These equations include the partial differentiations of an …

Divergence-free meshless local Petrov–Galerkin method for Stokes flow

M Najafi, M Dehghan, B Šarler, G Kosec… - Engineering with …, 2022‏ - Springer
The purpose of the present paper is development of an efficient meshless solution of steady
incompressible Stokes flow problems with constant viscosity in two dimensions, with …

Divergence-free interpolation of vector fields from point values — exact ∇ ⋅B = 0 in numerical simulations

CP McNally - Monthly Notices of the Royal Astronomical Society …, 2011‏ - academic.oup.com
In astrophysical magnetohydrodynamics (MHD) and electrodynamics simulations,
numerically enforcing the∇· B= 0 constraint on the magnetic field has been difficult. We …

Matrix-valued radial basis functions: stability estimates and applications

S Lowitzsch - Advances in Computational Mathematics, 2005‏ - Springer
Radial basis functions (RBFs) have found important applications in areas such as signal
processing, medical imaging, and neural networks since the early 1980's. Several …

Sobolev-type approximation rates for divergence-free and curl-free RBF interpolants

E Fuselier - Mathematics of Computation, 2008‏ - ams.org
Recently, error estimates have been made available for divergence-free radial basis
function (RBF) interpolants. However, these results are only valid for functions within the …

Divergence-free RBFs on surfaces

FJ Narcowich, JD Ward, GB Wright - Journal of Fourier Analysis and …, 2007‏ - Springer
This article presents a new tool for fitting a divergence-free vector field tangent to a two-
dimensional orientable surface P∈\BbbR^3 to samples of such a field taken at scattered …