Monomial augmentation guidelines for RBF-FD from accuracy versus computational time perspective

DOI10.1007/s10915-020-01401-yzbMath1466.65213arXiv1909.01126OpenAlexW3131419467MaRDI QIDQ1996005

Gregor Kosec, Mitja Jančič, Jure Slak

Publication date: 2 March 2021

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.01126

zbMATH Keywords

convergence ratesPoisson's equationmeshless methodsoptimal order\(n\)-dimensionalRBF-FD

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Finite difference methods for boundary value problems involving PDEs (65N06) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Numerical radial basis function approximation (65D12)

Related Items (2)

Guidelines for RBF-FD discretization: numerical experiments on the interplay of a multitude of parameter choices ⋮ Residual viscosity stabilized RBF-FD methods for solving nonlinear conservation laws

Uses Software

• Eigen
• Mfree2D
• Medusa

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the role of polynomials in RBF-FD approximations: II. Numerical solution of elliptic PDEs
• Stable computations with flat radial basis functions using vector-valued rational approximations
• On using radial basis functions in a ``finite difference mode with applications to elasticity problems
• On the role of polynomials in RBF-FD approximations. I: Interpolation and accuracy
• Refined meshless local strong form solution of Cauchy-Navier equation on an irregular domain
• Radial basis function generated finite differences for option pricing problems
• Adaptive RBF-FD method for elliptic problems with point singularities in 2D
• Hyperviscosity-based stabilization for radial basis function-finite difference (RBF-FD) discretizations of advection-diffusion equations
• Fast generation of 2-D node distributions for mesh-free PDE discretizations
• An insight into RBF-FD approximations augmented with polynomials
• Equivalent-PDE based stabilization of strong-form meshless methods applied to advection-dominated problems
• Local RBF method for multi-dimensional partial differential equations
• On Haar's Theorem Concerning Chebychev Approximation Problems Having Unique Solutions
• A Primer on Radial Basis Functions with Applications to the Geosciences
• Smooth interpolation of large sets of scattered data
• A FINITE POINT METHOD IN COMPUTATIONAL MECHANICS. APPLICATIONS TO CONVECTIVE TRANSPORT AND FLUID FLOW
• Robust Node Generation for Mesh-free Discretizations on Irregular Domains and Surfaces
• On Generation of Node Distributions for Meshless PDE Discretizations
• Solving PDEs with radial basis functions
• A general advancing front technique for filling space with arbitrary objects
• Scattered Data Approximation

This page was built for publication: Monomial augmentation guidelines for RBF-FD from accuracy versus computational time perspective