Solution of the Cauchy problem for the wave equation using iterative regularization

DOI10.1080/17415977.2021.1949590OpenAlexW3170506392MaRDI QIDQ5861305

M. Alosaimi, B. Tomas Johansson, Daniel Lesnic

Publication date: 4 March 2022

Published in: Inverse Problems in Science and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17415977.2021.1949590

zbMATH Keywords

wave equationinverse problemregularizationCauchy problemconjugate gradient method

Mathematics Subject Classification ID

Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32)

Related Items (1)

A data completion algorithm using an integral representation of the Steklov-Poincaré operator

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Application of mixed formulations of quasi-reversibility to solve ill-posed problems for heat and wave equations: the 1D case
• On the Cauchy problem for semilinear elliptic equations
• Inverse space-dependent force problems for the wave equation
• A pseudo-extractor approach to hidden boundary regularity for the wave equation with mixed boundary conditions
• Boundary estimation of hyperbolic bio-heat conduction
• An inverse hyperbolic heat conduction problem in estimating surface heat flux of a living skin tissue
• Wave propagation from lateral Cauchy data using a boundary element method
• Splitting-based conjugate gradient method for a multi-dimensional linear inverse heat conduction problem
• A timelike Cauchy problem and an inverse problem for general hyperbolic equations
• Analysis and solution of the ill-posed inverse heat conduction problem
• The mixed Dirichlet-Neumann-Cauchy problem for second order hyperbolic operators
• The inverse problem of electrocardiography: A solution in terms of single- and double-layer sources on the epicardial surface
• A boundary integral equation method for numerical solution of parabolic and hyperbolic Cauchy problems
• Iterative Tikhonov regularization for the Cauchy problem for the Helmholtz equation
• A method of fundamental solutions for heat and wave propagation from lateral Cauchy data
• Carleman estimates for the regularization of ill-posed Cauchy problems
• Estimating the boundary condition in a 3D inverse hyperbolic heat conduction problem
• Iterative methods for an inverse heat conduction problem
• The Quasi-Reversibility Method for Thermoacoustic Tomography in a Heterogeneous Medium
• Numerical solution of a time-like Cauchy problem for the wave equation
• A noncharacteristic cauchy problem for linear parabolic equations II: a variational method
• The Cauchy problem for Laplace's equation via the conjugate gradient method
• An inverse space-dependent source problem for hyperbolic equations and the Lipschitz-like convergence of the quasi-reversibility method
• A boundary element method for a multi-dimensional inverse heat conduction problem
• A Nonlinear Conjugate Gradient Method with a Strong Global Convergence Property
• Function minimization by conjugate gradients
• Numerical solution of inverse heat conduction problems in two spatial dimensions
• Dirichlet, Neumann, and mixed boundary value problems for the wave equationu_xx—u_yy=0 for a rectangle
• Methods of conjugate gradients for solving linear systems
• Inverse problems for partial differential equations

This page was built for publication: Solution of the Cauchy problem for the wave equation using iterative regularization