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[PDF][PDF] Multiquadric radial basis function approximation methods for the numerical solution of partial differential equations
Radial Basis Function (RBF) methods have become the primary tool for interpolating
multidimensional scattered data. RBF methods also have become important tools for solving …
multidimensional scattered data. RBF methods also have become important tools for solving …
Model-based calibration for magnetic manipulation
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 …
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 …
require the approximation of functions that depend on many variables. This can be for a …
Divergence-free kernel methods for approximating the Stokes problem
We develop a new discretization scheme for the Stokes equations using analytically
divergence-free approximation spaces. Our scheme is based upon a meshfree method …
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
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 …
differential equations is proposed. These equations include the partial differentiations of an …
Divergence-free meshless local Petrov–Galerkin method for Stokes flow
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 …
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 …
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 …
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 …
function (RBF) interpolants. However, these results are only valid for functions within the …
Divergence-free RBFs on surfaces
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 …
dimensional orientable surface P∈\BbbR^3 to samples of such a field taken at scattered …