An adaptive method of fundamental solutions for solving the Laplace equation

DOI10.1016/j.camwa.2018.11.021zbMath1442.65439OpenAlexW2905518890WikidataQ128756607 ScholiaQ128756607MaRDI QIDQ2203890

Jaeyoun Oh, Zhuo-Jia Fu, Hui-Qing Zhu

Publication date: 2 October 2020

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2018.11.021

zbMATH Keywords

Laplace equationadaptive methodmethod of fundamental solutionserror estimator

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Green's functions for elliptic equations (35J08) Fundamental solutions, Green's function methods, etc. for boundary value problems involving PDEs (65N80)

Related Items (6)

The method of fundamental solutions for the scattering problem of an open cavity ⋮ Moving pseudo-boundary method of fundamental solutions for nonlinear potential problems ⋮ Analysis of an augmented moving least squares approximation and the associated localized method of fundamental solutions ⋮ An overview of the method of fundamental solutions -- solvability, uniqueness, convergence, and stability ⋮ Efficient numerical solution of boundary identification problems: MFS with adaptive stochastic optimization ⋮ On the determination of locating the source points of the MFS using effective condition number

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On choosing the location of the sources in the MFS
• On the choice of source points in the method of fundamental solutions
• A method of fundamental solutions without fictitious boundary
• Some remarks concerning the shape of the source contour with application of the method of fundamental solutions to elastic torsion of prismatic rods
• Fast simulation of multi-dimensional wave problems by the sparse scheme of the method of fundamental solutions
• The method of fundamental solutions for problems in potential flow
• Stability and convergence of the method of fundamental solutions for Helmholtz problems on analytic domains
• The method of fundamental solutions for elliptic boundary value problems
• The method of fundamental solutions for scattering and radiation problems.
• Application of a simulated annealing algorithm in the optimal placement of the source points in the method of the fundamental solutions
• The MFS versus the Trefftz method for the Laplace equation in 3D
• The adaptive algorithm for the selection of sources of the method of fundamental solutions
• Green's function formulation of Laplace's equation for electromagnetic crack detection
• An algorithm for selecting a good value for the parameter \(c\) in radial basis function interpolation
• On choosing ``optimal shape parameters for RBF approximation
• Fundamental Solutions Method for Elliptic Boundary Value Problems
• Vortex Element Methods for Fluid Dynamic Analysis of Engineering Systems
• The Approximate Solution of Elliptic Boundary-Value Problems by Fundamental Solutions
• Error Estimates for Adaptive Finite Element Computations
• Singular Boundary Method to Simulate Scattering of SH Wave by the Canyon Topography
• Application of the Method of Fundamental Solutions and the Generalized Lagally Theorem to the Interaction of Solid Body and External Singularities in An Inviscid Fluid
• The method of functional equations for the approximate solution of certain boundary value problems

This page was built for publication: An adaptive method of fundamental solutions for solving the Laplace equation