Singular boundary method for inverse heat conduction problems in general anisotropic media

DOI10.1080/17415977.2013.840300zbMath1329.65284OpenAlexW2061255104WikidataQ58011548 ScholiaQ58011548MaRDI QIDQ3465077

Wen Chen, Yan Gu, Zhuo-Jia Fu

Publication date: 28 January 2016

Published in: Inverse Problems in Science and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17415977.2013.840300

zbMATH Keywords

anisotropic heat conductioninverse Cauchy problemsingular boundary methodmeshless boundary collocation method

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Boundary element methods for boundary value problems involving PDEs (65N38) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21)

Related Items

Stability analysis of the Fourier–Bessel method for the Cauchy problem of the Helmholtz equation ⋮ A BEM formulation in conjunction with parametric equation approach for three-dimensional Cauchy problems of steady heat conduction ⋮ A new approximate method for an inverse time-dependent heat source problem using fundamental solutions and RBFs ⋮ A gradient-based regularization algorithm for the Cauchy problem in steady-state anisotropic heat conduction ⋮ BEM-fading regularization algorithm for Cauchy problems in 2D anisotropic heat conduction ⋮ Fading regularization MFS algorithm for the Cauchy problem in anisotropic heat conduction ⋮ Stable reconstruction of discontinuous solutions to the Cauchy problem in steady-state anisotropic heat conduction with non-smooth coefficients ⋮ Indirect boundary integral equation method for the Cauchy problem of the Laplace equation ⋮ Meshless Collocation Method for Inverse Source Identification Problems ⋮ A Regularized Singular Boundary Method for Inverse Cauchy Problem in Three-Dimensional Elastostatics ⋮ Numerical inversions for diffusion coefficients in two-dimensional space fractional diffusion equation

Cites Work

• Infinite domain potential problems by a new formulation of singular boundary method
• Solution of potential flow problems by the modified method of fundamental solutions: formulations with the single layer and the double layer fundamental solutions
• A method of fundamental solutions without fictitious boundary
• A new approach to free vibration analysis using boundary elements
• The method of fundamental solutions and condition number analysis for inverse problems of Laplace equation
• Some comments on the ill-conditioning of the method of fundamental solutions
• Desingularized meshless method for solving Laplace equation with over-specified boundary conditions using regularization techniques
• Solving the Laplace equation by meshless collocation using harmonic kernels
• The truncated SVD as a method for regularization
• The method of fundamental solutions for elliptic boundary value problems
• The use of Morozov's discrepancy principle for Tikhonov regularization for solving nonlinear ill-posed problems
• Regularization tools: A Matlab package for analysis and solution of discrete ill-posed problems
• Boundary collocation method for acoustic eigenanalysis of three-dimensional cavities using radial basis function
• Method of fundamental solutions with regularization techniques for Cauchy problems of elliptic operators
• Numerical solution of the Cauchy problem for steady-state heat transfer in two-dimensional functionally graded materials
• Novel meshless method for solving the potential problems with arbitrary domain
• A fundamental solution method for inverse heat conduction problem
• Investigation on near-boundary solutions by singular boundary method
• Boundary particle method for Cauchy inhomogeneous potential problems
• A survey of applications of the MFS to inverse problems
• Reconstruction of moving boundary for one-dimensional heat conduction equation by using the Lie-group shooting method
• The method of fundamental solutions for the inverse conductivity problem
• Morozov's discrepancy principle and Tikhonov-type functionals
• Recovering the source term in a linear diffusion problem by the method of fundamental solutions
• The Modified Truncated SVD Method for Regularization in General Form
• Practical Approximate Solutions to Linear Operator Equations When the Data are Noisy
• A simple method using Morozov's discrepancy principle for solving inverse scattering problems
• Regularized boundary element solution for an inverse boundary value problem in linear elasticity
• A fast algorithm for particle simulations