An inverse source identification by nonlinear optimization in a two-dimensional hyperbolic problem

DOI10.1080/17415977.2021.1904235OpenAlexW3155777179WikidataQ115549633 ScholiaQ115549633MaRDI QIDQ5036802

Faika Derya Şendur, Murat Subaşi, Cavide Yaşar

Publication date: 23 February 2022

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

Full work available at URL: https://doi.org/10.1080/17415977.2021.1904235

zbMATH Keywords

optimizationinverse problemshyperbolic equationsfinite elements method

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Initial-boundary value problems for first-order hyperbolic systems (35L50) Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain (34M50)

Cites Work

• Unnamed Item
• On optimal control of the hyperbolic equation coefficients
• A variational technique for optimal boundary control in a hyperbolic problem
• On ill-posedness and a Tikhonov regularization for a multidimensional inverse hyperbolic problem
• Identification problem for the wave equation with Neumann data input and Dirichlet data observations
• Direct methods of solving multidimensional inverse hyperbolic problems.
• The usage of wave polynomials in solving direct and inverse problems for two-dimensional wave equation
• An Algorithm for Least-Squares Estimation of Nonlinear Parameters
• Newton’s Method with a Model Trust Region Modification
• Uniqueness and stable determination of forcing terms in linear partial differential equations with overspecified boundary data
• One new strategy for a priori choice of regularizing parameters in Tikhonov's regularization
• Trust Region Methods
• Maximization by Quadratic Hill-Climbing
• Relationship between representation formulas for unique regularized solutions of inverse source problems with final overdetermination and singular value decomposition of input-output operators
• A method for the solution of certain non-linear problems in least squares