Application of radial basis meshless methods to direct and inverse biharmonic boundary value problems

DOI10.1002/cnm.736zbMath1067.65117OpenAlexW2167571677MaRDI QIDQ4667805

Jichun Li

Publication date: 21 April 2005

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

Full work available at URL: https://doi.org/10.1002/cnm.736

zbMATH Keywords

inverse problemnumerical examplescollocationradial basis functionmeshless methodbiharmonic boundary value problem

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Boundary value problems for higher-order elliptic equations (35J40) Inverse problems for PDEs (35R30) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Biharmonic, polyharmonic functions and equations, Poisson's equation in two dimensions (31A30) Boundary value and inverse problems for harmonic functions in two dimensions (31A25)

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Uses Software

• Mfree2D

Cites Work

• A numerical study of some radial basis function based solution methods for elliptic PDEs
• Full-order convergence of a mixed finite element method for fourth-order elliptic equations
• Solving partial differential equations by collocation using radial basis functions
• Meshless methods: An overview and recent developments
• Inverse acoustic and electromagnetic scattering theory.
• Special issue: Radial basis functions and partial differential equations
• Multiquadrics -- a scattered data approximation scheme with applications to computational fluid-dynamics. II: Solutions to parabolic, hyperbolic and elliptic partial differential equations
• The method of fundamental solutions for the numerical solution of the biharmonic equation
• Continuous/discontinuous finite element approximations of fourth-order elliptic problems in structural and continuum mechanics with applications to thin beams and plates, and strain gradient elasticity
• A fundamental solution method for inverse heat conduction problem
• Backus-Gilbert algorithm for the Cauchy problem of the Laplace equation
• A numerical method for heat transfer problems using collocation and radial basis functions
• A radial basis meshless method for solving inverse boundary value problems
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