Publication:1047136

{{DISPLAYTITLE:Solving the Laplace equation by meshless collocation using harmonic kernels

DOI10.1007/s10444-008-9078-3zbMath1180.65161OpenAlexW4255620270MaRDI QIDQ1047136

Robert Schaback

Publication date: 4 January 2010

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10444-008-9078-3

zbMATH Keywords

convergencenumerical exampleserror boundsLaplace equationmethod of fundamental solutionsmeshless collocationharmonic kernels

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items

The method of fundamental solutions for the Helmholtz equation, Direct meshless kernel techniques for time-dependent equations, The MFS for the solution of harmonic boundary value problems with non-harmonic boundary conditions, Singular boundary method for inverse heat conduction problems in general anisotropic media, The meshless kernel-based method of lines for parabolic equations, Solving PDEs with a Hybrid Radial Basis Function: Power-Generalized Multiquadric Kernel, Covariance models and Gaussian process regression for the wave equation. Application to related inverse problems, On degeneracy and invariances of random fields paths with applications in Gaussian process modelling, Solving the 3D Laplace equation by meshless collocation via harmonic kernels, Comparisons of method of fundamental solutions, method of particular solutions and the MFS-QR; stability analysis, Radial basis approximation for Newtonian potentials, An approximation theorist's view on solving operator equations -- with special attention to Trefftz, MFS, MPS, and DRM methods, A numerical method for identifying heat transfer coefficient

Cites Work

• Unnamed Item
• Unnamed Item
• Sampling inequalities for infinitely smooth functions, with applications to interpolation and machine learning
• The method of fundamental solutions for elliptic boundary value problems
• Approximate interpolation with applications to selecting smoothing parameters
• Kernel techniques: From machine learning to meshless methods
• Sobolev bounds on functions with scattered zeros, with applications to radial basis function surface fitting
• Convergence of Unsymmetric Kernel‐Based Meshless Collocation Methods
• Scattered Data Approximation