A moving pseudo‐boundary method of fundamental solutions for void detection

DOI10.1002/num.21739zbMath1268.65161OpenAlexW1988091477WikidataQ59901304 ScholiaQ59901304MaRDI QIDQ4929264

Daniel Lesnic, Liviu Marin, Andreas Karageorghis

Publication date: 13 June 2013

Published in: Numerical Methods for Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: http://eprints.whiterose.ac.uk/81066/1/paper308.pdf

zbMATH Keywords

algorithminverse problemnumerical examplesLaplace equationnonlinear least-squares problemmethod of fundamental solutionsmoving pseudo-boundary methodvoid detection

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Fundamental solutions, Green's function methods, etc. for boundary value problems involving PDEs (65N80)

Related Items

Simultaneous numerical determination of a corroded boundary and its admittance, Defect detection using Cauchy data on a part of outer boundary of an elastic body, Automated hybrid singularity superposition and anchored grid pattern BEM algorithm for the solution of inverse geometric problems, On solving free surface problems in layered soil using the method of fundamental solutions, The MFS for the identification of a sound-soft interior acoustic scatterer, The method of fundamental solutions for the identification of a scatterer with impedance boundary condition in interior inverse acoustic scattering, Solution for the geometric elastostatic inverse problem by means of not completely overdetermined boundary data, An energy gap functional: cavity identification in linear elasticity, An efficient moving pseudo-boundary MFS for void detection, Moving pseudo-boundary method of fundamental solutions for nonlinear potential problems, Efficient numerical solution of boundary identification problems: MFS with adaptive stochastic optimization, On inverse problems for characteristic sources in Helmholtz equations, A meshless numerical identification of a sound-hard obstacle, The method of fundamental solutions for Brinkman flows. I: Exterior domains, The method of fundamental solutions for Brinkman flows. II: Interior domains, The method of fundamental solutions for the two-dimensional inverse Stefan problem, The Method of Fundamental Solutions in Solving Coupled Boundary Value Problems for M/EEG

Uses Software

• Matlab
• HYBRJ
• minpack

Cites Work

• Unnamed Item
• Some remarks concerning the shape of the source contour with application of the method of fundamental solutions to elastic torsion of prismatic rods
• An iterative MFS approach for the detection of immersed obstacles
• The method of fundamental solutions for problems in potential flow
• On the convergence of interior-reflective Newton methods for nonlinear minimization subject to bounds
• The method of fundamental solutions for the numerical solution of the biharmonic equation
• The MFS for numerical boundary identification in two-dimensional harmonic problems
• Nonlinear integral equations for solving inverse boundary value problems for inclusions and cracks
• Steady-state nonlinear heat conduction in composite materials using the method of fundamental solutions
• A survey of applications of the MFS to inverse problems
• Detection of cavities using the method of fundamental solutions
• The Method of Fundamental Solutions for the Solution of Nonlinear Plane Potential Problems
• The Approximate Solution of Elliptic Boundary-Value Problems by Fundamental Solutions
• The Method of Fundamental Solutions for Stokes flows with a free surface
• The method of fundamental solutions for axisymmetric potential problems
• The Use of the L-Curve in the Regularization of Discrete Ill-Posed Problems
• An Interior Trust Region Approach for Nonlinear Minimization Subject to Bounds
• Discrete Inverse Problems
• Potential field based geometric modelling using the method of fundamental solutions
• Conformal mappings and inverse boundary value problems
• The method of functional equations for the approximate solution of certain boundary value problems
• A method for the approximate solution of limiting problems in mathematical physics
• Optimal stability for the inverse problem of multiple cavities