Boundary element-minimal error method for the Cauchy problem associated with Helmholtz-type equations

DOI10.1007/s00466-009-0368-5zbMath1185.74097OpenAlexW2066097596MaRDI QIDQ1027818

Liviu Marin

Publication date: 30 June 2009

Published in: Computational Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00466-009-0368-5

zbMATH Keywords

iterative algorithminverse problemregularization

Mathematics Subject Classification ID

Boundary element methods applied to problems in solid mechanics (74S15)

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Cites Work

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• The plane wave method for inverse problems associated with Helmholtz-type equations
• The method of fundamental solutions for inverse boundary value problems associated with the two-dimensional biharmonic equation
• A minimal error conjugate gradient method for ill-posed problems
• An alternating iterative algorithm for the Cauchy problem associated to the Helmholtz equation
• Conjugate gradient-boundary element solution to the Cauchy problem for Helmholtz-type equations
• A meshless method for the numerical solution of the Cauchy problem associated with three-dimensional Helmholtz-type equations
• Boundary knot method for the Cauchy problem associated with the inhomogeneous Helmholtz equation
• Two approximate methods of a Cauchy problem for the Helmholtz equation
• A meshless method for some inverse problems associated with the Helmholtz equation
• The minimal error method for the Cauchy problem in linear elasticity. Numerical implementation for two-dimensional homogeneous isotropic linear elasticity
• BEM solution for the Cauchy problem associated with Helmholtz-type equations by the Landweber method
• Modified Tikhonov regularization method for the Cauchy problem of the Helmholtz equation
• The Detection of the Source of Acoustical Noise in Two Dimensions
• Iterative methods for an inverse heat conduction problem
• Dual reciprocity boundary element method solution of the Cauchy problem for Helmholtz-type equations with variable coefficients
• Conjugate Gradient-Boundary Element Method for the Cauchy Problem in Elasticity
• Comparison of regularization methods for solving the Cauchy problem associated with the Helmholtz equation
• Boundary knot method for some inverse problems associated with the Helmholtz equation
• A variational conjugate gradient method for determining the fluid velocity of a slow viscous flow
• Numerical solution of an inverse 2D Cauchy problem connected with the Helmholtz equation
• The detection of surface vibrations from interior acoustical pressure
• The Cauchy problem for Laplace's equation via the conjugate gradient method
• The regularizing properties of the adjoint gradient method in ill-posed problems
• Regularized boundary element solution for an inverse boundary value problem in linear elasticity
• The Minimal Error Conjugate Gradient Method is a Regularization Method
• An iterative method for the reconstruction of a stationary flow
• Reconstruction of a stationary flow from incomplete boundary data using iterative methods
• An Iteration Formula for Fredholm Integral Equations of the First Kind

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