On a quasi-reversibility regularization method for a Cauchy problem of the Helmholtz equation

DOI10.1016/j.cam.2009.09.031zbMath1185.65171OpenAlexW2010184596MaRDI QIDQ2654204

Ailin Qian, Xiang-Tuan Xiong, Yu-Jiang Wu

Publication date: 15 January 2010

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2009.09.031

zbMATH Keywords

convergenceregularizationCauchy problemHelmholtz equationill-posed problemquasi-reversibility

Mathematics Subject Classification ID

Ill-posed problems for PDEs (35R25) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs (65M30)

Related Items (21)

Regularization method for an ill-posed Cauchy problem for elliptic equations ⋮ An a posteriori truncation method for some Cauchy problems associated with Helmholtz-type equations ⋮ Recovery the interior temperature of a nonhomogeneous elliptic equation from boundary data ⋮ A new general filter regularization method for Cauchy problems for elliptic equations with a locally Lipschitz nonlinear source ⋮ On stochastic elliptic equations driven by Wiener process with non-local condition ⋮ An effective relaxed alternating procedure for Cauchy problem connected with Helmholtz Equation ⋮ Optimal error bound and a quasi-boundary value regularization method for a Cauchy problem of the modified Helmholtz equation ⋮ A meshless method for solving the nonlinear inverse Cauchy problem of elliptic type equation in a doubly-connected domain ⋮ A regularization method for solving the Cauchy problem for the Helmholtz equation ⋮ A novel mixed group preserving scheme for the inverse Cauchy problem of elliptic equations in annular domains ⋮ A spectral regularization method for a Cauchy problem of the modified Helmholtz equation ⋮ A regularization method for the elliptic equation with inhomogeneous source ⋮ A homogenization function technique to solve the 3D inverse Cauchy problem of elliptic type equations in a closed walled shell ⋮ A non-typical Lie-group integrator to solve nonlinear inverse Cauchy problem in an arbitrary doubly-connected domain ⋮ An order optimal regularization method for the Cauchy problem of a Laplace equation in an annulus domain ⋮ An improved iteration regularization method and application to reconstruction of dynamic loads on a plate ⋮ A \textit{a posteriori} regularization for the Cauchy problem for the Helmholtz equation with inhomogeneous Neumann data ⋮ Nonparametric regression in a statistical modified Helmholtz equation using the Fourier spectral regularization ⋮ Regularization methods for identifying the initial value of time fractional pseudo-parabolic equation ⋮ Three regularization methods for identifying the initial value of time fractional advection-dispersion equation ⋮ A mollification method for a Cauchy problem for the Helmholtz equation

Cites Work

• The method of fundamental solutions for inverse boundary value problems associated with the two-dimensional biharmonic equation
• Modified regularization method for the Cauchy problem of the Helmholtz equation
• 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
• Method of fundamental solutions with regularization techniques for Cauchy problems of elliptic operators
• BEM solution for the Cauchy problem associated with Helmholtz-type equations by the Landweber method
• Comparison of regularization methods for solving the Cauchy problem associated with the Helmholtz equation

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