Dimension-splitting data points redistribution for meshless approximation

Authors:
Ting-On Kwok;Leevan Ling
Affiliations:
-;-
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

Citing 13
Cited 0

A numerical study of three moving-grid methods for one-dimensional partial differential equations which are based on the method of lines

Journal of Computational Physics
A Study of Monitor Functions for Two-Dimensional Adaptive Mesh Generation

SIAM Journal on Scientific Computing
Adaptive mesh movement — the MMPDE approach and its applications

Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
Practical aspects of formulation and solution of moving mesh partial differential equations

Journal of Computational Physics
Moving mesh methods in multiple dimensions based on harmonic maps

Journal of Computational Physics
Computational solution of two-dimensional unsteady PDEs using moving mesh methods

Journal of Computational Physics
Adaptive Mesh Methods for One- and Two-Dimensional Hyperbolic Conservation Laws

SIAM Journal on Numerical Analysis
Approaches for generating moving adaptive meshes: location versus velocity

Applied Numerical Mathematics - Special issue: 2nd international workshop on numerical linear algebra, numerical methods for partial differential equations and optimization
Adaptive moving mesh computations for reaction--diffusion systems

Journal of Computational and Applied Mathematics - Special issue: Selected papers from the 2nd international conference on advanced computational methods in engineering (ACOMEN2002) Liege University, Belgium, 27-31 May 2002
On Resistive MHD Models with Adaptive Moving Meshes

Journal of Scientific Computing
A splitting moving mesh method for reaction-diffusion equations of quenching type

Journal of Computational Physics
A robust moving mesh finite volume method applied to 1D hyperbolic conservation laws from magnetohydrodynamics

Journal of Computational Physics
The role of the multiquadric shape parameters in solving elliptic partial differential equations

Computers & Mathematics with Applications

Quantified Score

Hi-index	7.29

Visualization

Abstract

To better approximate nearly singular functions with meshless methods, we propose a data points redistribution method extended from the well-known one-dimensional equidistribution principle. With properly distributed data points, nearly singular functions can be well approximated by linear combinations of global radial basis functions. The proposed method is coupled with an adaptive trial subspace selection algorithm in order to reduce computational cost. In our numerical examples, clear exponential convergence (with respect to the numbers of data points) can be observed.