A meshless method for solving the Cauchy problem in three-dimensional elastostatics

DOI10.1016/j.camwa.2005.02.009zbMath1127.74014OpenAlexW1996743104MaRDI QIDQ814071

Liviu Marin

Publication date: 2 February 2006

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

Full work available at URL: https://doi.org/10.1016/j.camwa.2005.02.009

zbMATH Keywords

inverse problemregularizationCauchy problemelastostaticsmethod of fundamental solutionsmeshless method

Mathematics Subject Classification ID

Ill-posedness and regularization problems in numerical linear algebra (65F22) Classical linear elasticity (74B05) Numerical approximation of solutions of equilibrium problems in solid mechanics (74G15) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

Related Items (36)

The direct method of fundamental solutions and the inverse Kirsch-Kress method for the reconstruction of elastic inclusions or cavities ⋮ Estimation of effective elastic moduli of random structure composites by the method of fundamental solutions ⋮ A local meshless method based on the finite collocation and local integral equations method for delay PDEs ⋮ A meshless method for solving 1D time-dependent heat source problem ⋮ Inverse heat conduction problem in two-dimensional anisotropic medium ⋮ Boundary reconstruction in two-dimensional steady state anisotropic heat conduction using a regularized meshless method ⋮ Convergence analysis for the Cauchy problem of Laplace's equation by a regularized method of fundamental solutions ⋮ A meshless singular boundary method for three‐dimensional elasticity problems ⋮ Regularized method of fundamental solutions for boundary identification in two-dimensional isotropic linear elasticity ⋮ Relaxation procedures for an iterative MFS algorithm for the stable reconstruction of elastic fields from Cauchy data in two-dimensional isotropic linear elasticity ⋮ The minimal error method for the Cauchy problem in linear elasticity. Numerical implementation for two-dimensional homogeneous isotropic linear elasticity ⋮ The MFS for numerical boundary identification in two-dimensional harmonic problems ⋮ Relaxation procedures for an iterative MFS algorithm for two-dimensional steady-state isotropic heat conduction Cauchy problems ⋮ The Cauchy problem for the 3D Poisson equation: Landweber iteration vs. horizontally diagonalize and fit method ⋮ A meshless method for the stable solution of singular inverse problems for two-dimensional Helmholtz-type equations ⋮ Inverse source identification by Green's function ⋮ An inverse boundary problem for one-dimensional heat equation with a multilayer domain ⋮ Adaptive error estimation technique of the Trefftz method for solving the over-specified boundary value problem ⋮ An overview of the method of fundamental solutions -- solvability, uniqueness, convergence, and stability ⋮ A relaxation method of an alternating iterative algorithm for the Cauchy problem in linear isotropic elasticity ⋮ An iterative method for the Cauchy problem in linear elasticity with fading regularization effect ⋮ Interface integral technique for the thermoelasticity of random structure matrix composites ⋮ Non-iterative regularized MFS solution of inverse boundary value problems in linear elasticity: a numerical study ⋮ An invariant method of fundamental solutions for the Cauchy problem in two-dimensional isotropic linear elasticity ⋮ Analysis of Two-Dimensional Thin Structures (From Micro- to Nano-Scales) Using the Singular Boundary Method ⋮ A Regularized Singular Boundary Method for Inverse Cauchy Problem in Three-Dimensional Elastostatics ⋮ Localized Method of Fundamental Solutions for Three-Dimensional Elasticity Problems: Theory ⋮ Solution of Cauchy Problems by the Multiple Scale Method of Particular Solutions Using Polynomial Basis Functions ⋮ A survey of applications of the MFS to inverse problems ⋮ An alternating iterative MFS algorithm for the Cauchy problem for the modified Helmholtz equation ⋮ A numerical study of the SVD–MFS solution of inverse boundary value problems in two‐dimensional steady‐state linear thermoelasticity ⋮ Simultaneous determination for a space-dependent heat source and the initial data by the MFS ⋮ Numerical identification for impedance coefficient by a MFS-based optimization method ⋮ Reconstruction of a moving boundary from Cauchy data in one-dimensional heat equation ⋮ Analysis of three-dimensional anisotropic heat conduction problems on thin domains using an advanced boundary element method ⋮ A numerical study on the solution of the Cauchy problem in elasticity

Uses Software

• Regularization tools
• UTV

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The method of fundamental solutions for the Cauchy problem in two-dimensional linear elasticity
• An iterative boundary element algorithm for a singular Cauchy problem in linear elasticity
• The method of fundamental solutions for inverse boundary value problems associated with the two-dimensional biharmonic equation
• Methods of fundamental solutions for harmonic and biharmonic boundary value problems
• The method of fundamental solutions for inhomogeneous elliptic problems
• A particular solution Trefftz method for nonlinear Poisson problems in heat and mass transfer
• The method of fundamental solutions for elliptic boundary value problems
• The method of fundamental solutions for axisymmetric elasticity problems
• A numerical computation for inverse boundary determination problem
• The method of fundamental solutions for layered elastic materials
• An operator splitting-radial basis function method for the solution of transient nonlinear Poisson problems
• The method of fundamental solutions for the numerical solution of the biharmonic equation
• Boundary element solution for the Cauchy problem in linear elasticity using singular value decomposition
• Limitations of the \(L\)-curve method in ill-posed problems
• Conjugate Gradient-Boundary Element Method for the Cauchy Problem in Elasticity
• Fundamental Solutions Method for Elliptic Boundary Value Problems
• Fundamental solutions for the collocation method in three-dimensional elastostatics
• The Approximate Solution of Elliptic Boundary-Value Problems by Fundamental Solutions
• An Inverse Problem in Elasticity With Partially Overprescribed Boundary Conditions, Part I: Theoretical Approach
• A radial basis meshless method for solving inverse boundary value problems
• The method of fundamental solutions for heat conduction in layered materials
• Non-convergence of the L-curve regularization parameter selection method
• Method of fundamental solutions: singular value decomposition analysis
• Regularized boundary element solution for an inverse boundary value problem in linear elasticity
• The method of functional equations for the approximate solution of certain boundary value problems
• The numerical solution of three-dimensional Signorini problems with the method of fundamental solutions
• The method of fundamental solutions for the calculation of the eigenvalues of the Helmholtz equation
• Boundary element method for the Cauchy problem in linear elasticity.

This page was built for publication: A meshless method for solving the Cauchy problem in three-dimensional elastostatics