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Journal of Scientific Computing

Erschienen in:

01.06.2021

The Quasi-reversibility Method to Numerically Solve an Inverse Source Problem for Hyperbolic Equations

verfasst von: Thuy T. Le, Loc H. Nguyen, Thi-Phong Nguyen, William Powell

Erschienen in: Journal of Scientific Computing | Ausgabe 3/2021

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Abstract

We propose a numerical method to solve an inverse source problem of computing the initial condition of hyperbolic equations from the measurements of Cauchy data. This problem arises in thermo- and photo-acoustic tomography in a bounded cavity, in which the reflection of the wave makes the widely-used approaches, such as the time reversal method, not applicable. In order to solve this inverse source problem, we approximate the solution to the hyperbolic equation by its Fourier series with respect to a special orthonormal basis of \(L^2\). Then, we derive a coupled system of elliptic equations for the corresponding Fourier coefficients. We solve it by the quasi-reversibility method. The desired initial condition follows. We rigorously prove the convergence of the quasi-reversibility method as the noise level tends to 0. Some numerical examples are provided. In addition, we numerically prove that the use of the special basic above is significant.

Vorheriger Artikel Unconditional Optimal Error Estimates of Linearized, Decoupled and Conservative Galerkin FEMs for the Klein–Gordon–Schrödinger Equation

Nächster Artikel Convergence Analysis of Hybrid High-Order Methods for the Wave Equation

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Titel: The Quasi-reversibility Method to Numerically Solve an Inverse Source Problem for Hyperbolic Equations
verfasst von: Thuy T. Le
Loc H. Nguyen
Thi-Phong Nguyen
William Powell
Publikationsdatum: 01.06.2021
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 3/2021
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-021-01501-3

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