Direct approximation on spheres using generalized moving least squares

DOI10.1007/S10543-017-0659-8zbMath1407.65312OpenAlexW2611363983MaRDI QIDQ1689314

Davoud Mirzaei

Publication date: 12 January 2018

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10543-017-0659-8

zbMATH Keywords

spherical harmonicsmoving least squaresLaplace-Beltrami operatorslocal polynomial reproduction

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Approximation by polynomials (41A10)

Related Items (8)

A Petrov–Galerkin RBF method for diffusion equation on the unit sphere ⋮ Approximation of continuous surface differential operators with the generalized moving least-squares (GMLS) method for solving reaction-diffusion equation ⋮ Numerical simulation of a prostate tumor growth model by the RBF-FD scheme and a semi-implicit time discretization ⋮ A divergence-free generalized moving least squares approximation with its application ⋮ A meshless technique based on generalized moving least squares combined with the second-order semi-implicit backward differential formula for numerically solving time-dependent phase field models on the spheres ⋮ Numerical simulation and error estimation of the time-dependent Allen-Cahn equation on surfaces with radial basis functions ⋮ A weak-form RBF-generated finite difference method ⋮ Simulation of Maxwell equation based on an ADI approach and integrated radial basis function-generalized moving least squares (IRBF-GMLS) method with reduced order algorithm based on proper orthogonal decomposition

Uses Software

• rbf_qr

Cites Work

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• Surfaces Generated by Moving Least Squares Methods
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• Element‐free Galerkin methods
• Error Analysis of Nodal Meshless Methods
• Efficient Spherical Designs with Good Geometric Properties
• Approximation Theory and Harmonic Analysis on Spheres and Balls
• Solving PDEs with radial basis functions
• Scattered Data Approximation
• Interpolation by polynomials and radial basis functions on spheres

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