A computational method to estimate the unknown coefficient in a wave equation using boundary measurements

DOI10.1080/17415977.2011.559655zbMath1252.65160OpenAlexW2010902543MaRDI QIDQ3111166

Wenyuan Liao

Publication date: 18 January 2012

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

Full work available at URL: https://doi.org/10.1080/17415977.2011.559655

zbMATH Keywords

parameter estimationwave equationinverse problemnumerical examplesfinite difference schemeoptimization algorithmsacoustic coefficientauto differentiation

Mathematics Subject Classification ID

Inverse problems for PDEs (35R30) Wave equation (35L05) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32)

Related Items (7)

Application of the Ritz-Galerkin method for recovering the spacewise-coefficients in the wave equation ⋮ A computational method for full waveform inversion of crosswell seismic data using automatic differentiation ⋮ A fourth-order compact difference scheme for the parabolic inverse problem with an overspecification at a point ⋮ Determination of space–time-dependent heat source in a parabolic inverse problem via the Ritz–Galerkin technique ⋮ Reconstruction of a time‐dependent coefficient in nonlinear Klein–Gordon equation using Bernstein spectral method ⋮ An adjoint-based Jacobi-type iterative method for elastic full waveform inversion problem ⋮ An efficient fourth-order low dispersive finite difference scheme for a 2-D acoustic wave equation

Uses Software

• L-BFGS
• TAPENADE
• TAMC

Cites Work

• Fourth order schemes for the heterogeneous acoustics equation
• Numerical methods for viscous and nonviscous wave equations
• High-order schemes for acoustic waveform simulation
• On the limited memory BFGS method for large scale optimization
• An iterative method for simultaneous determination of bulk and shear moduli and density variations
• The free bending vibration of cylindrical tank partially filled with liquid and submerged in water
• Compact finite difference schemes with spectral-like resolution
• Higher order accurate difference solutions of fluid mechanics problems by a compact differencing technique
• Highly accurate compact implicit methods and boundary conditions
• About the stability of the inverse problem in 1-D wave equations application to the interpretation of seismic profiles
• Global Lipschitz stability in an inverse hyperbolic problem by interior observations
• An inverse problem for the acoustic wave equation with finite sets of boundary data
• A new iterative method for solving the coefficient inverse problem of the wave equation
• A Modified Equation Approach to Constructing Fourth Order Methods for Acoustic Wave Propagation
• Recipes for adjoint code construction
• Global Convergence Properties of Conjugate Gradient Methods for Optimization
• Direct numerical method for an inverse problem of hyperbolic equations
• Determination of a coefficient in an acoustic equation with a single measurement
• Construction Analysis of Fourth-Order Finite Difference Schemes for the Acoustic Wave Equation in Nonhomogeneous Media

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