A DISCREPANCY PRINCIPLE FOR THE SOURCE POINTS LOCATION IN USING THE MFS FOR SOLVING THE BHCP

DOI10.1142/S0219876209001759zbMath1264.80031OpenAlexW2146572382MaRDI QIDQ4924245

Ming Li, Benny Y. C. Hon

Publication date: 31 May 2013

Published in: International Journal of Computational Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219876209001759

zbMATH Keywords

backward heat conduction problemmethod of fundamental solutions

Mathematics Subject Classification ID

Fundamental solutions, Green's function methods, etc. for initial value and initial-boundary value problems involving PDEs (65M80)

Related Items

A vector regularization method to solve linear inverse problems ⋮ Shape Reconstruction of Conductivity Interface Problems ⋮ A double optimal descent algorithm for iteratively solving ill-posed linear inverse problems ⋮ DeepBHCP: deep neural network algorithm for solving backward heat conduction problems ⋮ Reducing the ill conditioning in the method of fundamental solutions ⋮ Shannon wavelet regularization methods for a backward heat equation ⋮ Inverse source identification by Green's function ⋮ A meshless method based on RBFs method for nonhomogeneous backward heat conduction problem ⋮ On regularization and error estimates for the backward heat conduction problem with time-dependent thermal diffusivity factor ⋮ Optimally scaled vector regularization method to solve ill-posed linear problems ⋮ A comparative study on applying the method of fundamental solutions to the backward heat conduction problem ⋮ Optimal algorithms in a Krylov subspace for solving linear inverse problems by MFS ⋮ Numerical computation for backward time-fractional diffusion equation ⋮ The method of fundamental solutions for a time-dependent two-dimensional Cauchy heat conduction problem ⋮ A Trefftz method in space and time using exponential basis functions: application to direct and inverse heat conduction problems ⋮ A method of fundamental solutions for radially symmetric and axisymmetric backward heat conduction problems ⋮ A method of fundamental solutions for two-dimensional heat conduction ⋮ A numerical algorithm to reduce ill-conditioning in meshless methods for the Helmholtz equation ⋮ A survey of applications of the MFS to inverse problems ⋮ Fundamental kernel-based method for backward space-time fractional diffusion problem ⋮ Numerical solution of three-dimensional backward heat conduction problems by the time evolution method of fundamental solutions ⋮ A radial basis function (RBF)-finite difference (FD) method for the backward heat conduction problem ⋮ A globally optimal tri-vector method to solve an ill-posed linear system ⋮ A doubly optimized solution of linear equations system expressed in an affine Krylov subspace ⋮ Advances in the greedy optimization algorithm for nodes and collocation points using the method of fundamental solutions ⋮ Kernel-based approximation for Cauchy problem of the time-fractional diffusion equation ⋮ Analytic series solutions of 2D forward and backward heat conduction problems in rectangles and a new regularization ⋮ A well-conditioned method of fundamental solutions for Laplace equation ⋮ The method of fundamental solution for the inverse source problem for the space-fractional diffusion equation

Cites Work

• Unnamed Item
• Unnamed Item
• Fundamental solutions for second order linear elliptic partial differential equations
• The method of fundamental solutions for elliptic boundary value problems
• Regularization tools: A Matlab package for analysis and solution of discrete ill-posed problems
• The boundary element method for the solution of the backward heat conduction equation
• A study of regularization by monotonicity
• A fundamental solution method for inverse heat conduction problem
• Time-dependent fundamental solutions for homogeneous diffusion problems
• A Cauchy problem for the heat equation
• On the simulation source technique for exterior problems in acoustics
• The method of fundamental solutions for the backward heat conduction problem
• Remarks on choosing a regularization parameter using the quasi-optimality and ratio criterion
• Analysis of Discrete Ill-Posed Problems by Means of the L-Curve
• Numerical tools for analysis and solution of Fredholm integral equations of the first kind
• The Approximate Solution of Elliptic Boundary-Value Problems by Fundamental Solutions
• The Use of the L-Curve in the Regularization of Discrete Ill-Posed Problems
• The use of monotonicity for choosing the regularization parameter in ill-posed problems
• The method of functional equations for the approximate solution of certain boundary value problems