Approximate solution of a Cauchy problem for the Helmholtz equation

DOI10.1088/0266-5611/22/3/015zbMath1099.35160OpenAlexW2004861693MaRDI QIDQ5478597

Kazimierz Regiński, Teresa Regińska

Publication date: 13 July 2006

Published in: Inverse Problems (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/a72d2f647e8ba4d4f7e4e009db21b754f7c9ec75

zbMATH Keywords

stabilityconvergenceregularizationCauchy problemHelmholtz equation

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) PDEs in connection with optics and electromagnetic theory (35Q60) Ill-posed problems for PDEs (35R25) Theoretical approximation in context of PDEs (35A35) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Electromagnetic theory (general) (78A25)

Related Items (58)

Optimal control of the ill-posed Cauchy elliptic problem ⋮ Solving the Cauchy problem for the Helmholtz equation using cubic smoothing splines ⋮ Reconstruction of the electric field of the Helmholtz equation in three dimensions ⋮ Approximation of mild solutions of the linear and nonlinear elliptic equations ⋮ An Aitken-like acceleration method applied to missing boundary data reconstruction for the Cauchy-Helmholtz problem ⋮ Analysis and numerical simulation of the three-dimensional Cauchy problem for quasi-linear elliptic equations ⋮ Modification of Iterative Tikhonov Regularization Motivated by a Problem of Identification of Laser Beam Quality Parameters ⋮ The inverse source problem for time-fractional diffusion equation: stability analysis and regularization ⋮ An a posteriori truncation method for some Cauchy problems associated with Helmholtz-type equations ⋮ Regularization of the Cauchy problem for the Helmholtz equation by using Meyer wavelet ⋮ A modified integral equation method of the nonlinear elliptic equation with globally and locally Lipschitz source ⋮ An \textit{a posteriori} Fourier regularization method for identifying the unknown source of the space-fractional diffusion equation ⋮ A modified iterative regularization method for ill-posed problems ⋮ A modified method for a Cauchy problem of the Helmholtz equation ⋮ A new general filter regularization method for Cauchy problems for elliptic equations with a locally Lipschitz nonlinear source ⋮ An alternating iterative method for solving the Cauchy problem for the Helmholtz equation in Interior multiply connected domain ⋮ Local knot method for solving inverse Cauchy problems of Helmholtz equations on complicated two‐ and three‐dimensional domains ⋮ An optimal filtering method for the Cauchy problem of the Helmholtz equation ⋮ A regularization method for solving the Cauchy problem for the Helmholtz equation ⋮ The plane wave method for inverse problems associated with Helmholtz-type equations ⋮ An Inverse Diffraction Problem: Shape Reconstruction ⋮ A wavelet method for the Cauchy problem for the Helmholtz equation ⋮ Analysis of a Quasi-Reversibility Method for a Terminal Value Quasi-Linear Parabolic Problem with Measurements ⋮ A spectral regularization method for a Cauchy problem of the modified Helmholtz equation ⋮ Two iterative methods for a Cauchy problem of the elliptic equation with variable coefficients in a strip region ⋮ A posteriori regularization parameter choice rule for truncation method for identifying the unknown source of the Poisson equation ⋮ An iterative regularization method to solve the Cauchy problem for the Helmholtz equation ⋮ The truncation method for the Cauchy problem of the inhomogeneous Helmholtz equation ⋮ The truncation method for identifying the heat source dependent on a spatial variable ⋮ Conditional Stability Estimates for Ill-Posed PDE Problems by Using Interpolation ⋮ OPTIMAL ERROR BOUND AND APPROXIMATION METHODS FOR A CAUCHY PROBLEM OF THE MODIFIED HELMHOLTZ EQUATION ⋮ Fourier regularization method for solving a Cauchy problem for the Laplace equation ⋮ Wavelet moment method for the Cauchy problem for the Helmholtz equation ⋮ Two regularization methods for a Cauchy problem for the Laplace equation ⋮ Two regularization methods for the Cauchy problems of the Helmholtz equation ⋮ The truncation method for identifying an unknown source in the Poisson equation ⋮ An order optimal regularization method for the Cauchy problem of a Laplace equation in an annulus domain ⋮ Two regularization methods to identify time-dependent heat source through an internal measurement of temperature ⋮ The Cauchy problem of coupled elliptic sine-Gordon equations with noise: analysis of a general kernel-based regularization and reliable tools of computing ⋮ Iterative Tikhonov regularization for the Cauchy problem for the Helmholtz equation ⋮ An accelerated alternating procedure for the Cauchy problem for the Helmholtz equation ⋮ The Fourier regularization for solving the Cauchy problem for the Helmholtz equation ⋮ Regularization methods for a Cauchy problem for a parabolic equation in multiple dimensions ⋮ The truncation method for a two-dimensional nonhomogeneous backward heat problem ⋮ A \textit{a posteriori} regularization for the Cauchy problem for the Helmholtz equation with inhomogeneous Neumann data ⋮ Calculation of the heat flux near the liquid-gas-solid contact line ⋮ Modified Tikhonov regularization method for the Cauchy problem of the Helmholtz equation ⋮ Recursive linearization method for inverse medium scattering problems with complex mixture Gaussian error learning ⋮ A coupled complex boundary method for the Cauchy problem ⋮ An ill-posed boundary value problem for the Helmholtz equation on Lipschitz domains ⋮ Application of the cut-off projection to solve a backward heat conduction problem in a two-slab composite system ⋮ Conditional Stability Estimates and Regularization with Applications to Cauchy Problems for the Helmholtz Equation ⋮ Generalized Lavrentiev-type regularization method for the Cauchy problem of a semi-linear elliptic equation ⋮ Quasi-reversibility and truncation methods to solve a Cauchy problem for the modified Helmholtz equation ⋮ An alternating iterative procedure for the Cauchy problem for the Helmholtz equation ⋮ Robin–Dirichlet algorithms for the Cauchy problem for the Helmholtz equation ⋮ Comparative analysis of methods for regularizing an initial boundary value problem for the Helmholtz equation ⋮ A mollification method for a Cauchy problem for the Helmholtz equation

This page was built for publication: Approximate solution of a Cauchy problem for the Helmholtz equation