Radial basis functions for solving near singular Poisson problems

DOI10.1002/cnm.593zbMath1018.65131OpenAlexW2020388349MaRDI QIDQ4808445

Jichun Li, Ching-Shyang Chen, Günther Kuhn, Gennady S. Mishuris

Publication date: 22 May 2003

Published in: Communications in Numerical Methods in Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/cnm.593

zbMATH Keywords

particular solutionnumerical examplesradial basis functionsPoisson equationdual reciprocity methodmethod of fundamental solutionscompactly supported radial basis functionsnear singular problems

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)

Related Items

Applying multiquadric quasi-interpolation to solve Burgers' equation, A local meshless collocation method for solving certain inverse problems, Method of fundamental solutions for 3D elasticity with body forces by coupling compactly supported radial basis functions, Finite integration method with radial basis function for solving stiff problems, Solving partial differential equation by using multiquadric quasi-interpolation, An improved subspace selection algorithm for meshless collocation methods, The LMAPS Using Polynomial Basis Functions for Near-Singular Problems, On the selection of a good value of shape parameter in solving time-dependent partial differential equations using RBF approximation method, A time-efficient variable shape parameter Kansa-radial basis function method for the solution of nonlinear boundary value problems, The localized method of approximated particular solutions for near-singular two- and three-dimensional problems, A multiquadric quasi-interpolation with linear reproducing and preserving monotonicity, Particular Solution of Poisson Problems Using Cardinal Lagrangian Polyharmonic Splines, A multiple-scale higher order polynomial collocation method for 2D and 3D elliptic partial differential equations with variable coefficients

Cites Work

• Interpolation of scattered data: distance matrices and conditionally positive definite functions
• Multiquadrics - a scattered data approximation scheme with applications to computational fluid-dynamics. I: Surface approximations and partial derivative estimates
• Methods of fundamental solutions for harmonic and biharmonic boundary value problems
• The method of fundamental solutions for elliptic boundary value problems
• Particular solutions of 3D Helmholtz-type equations using compactly supported radial basis functions
• Particular solutions of Helmholtz-type operators using higher order polyharmonic splines
• Multistep scattered data interpolation using compactly supported radial basis functions
• The method of fundamental solutions for the numerical solution of the biharmonic equation
• Compactly supported positive definite radial functions
• Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree
• Some recent results and proposals for the use of radial basis functions in the BEM
• Solving differential equations with radial basis functions: Multilevel methods and smoothing
• Scattered Data Interpolation: Tests of Some Method
• Modified methods of fundamental solutions for harmonic and biharmonic problems with boundary singularities
• Dual reciprocity method using compactly supported radial basis functions
• Some comments on the use of radial basis functions in the dual reciprocity method
• Unnamed Item
• Unnamed Item
• Unnamed Item