Adjoint-state method for Hybridizable Discontinuous Galerkin discretization, application to the inverse acoustic wave problem

Faucher, Florian; Scherzer, Otmar

doi:10.1016/j.cma.2020.113406

Cited by 14 publications

(22 citation statements)

References 55 publications

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“…Our FWI-based reconstruction uses an iterative Newton-type method on an L 2 distance between data and simulations. For the discretization of the resulting partial differential equations, we use the hybridizable discontinuous Galerkin method (HDG), [8,18], and the open-source parallel software hawen 1 , [14].…”

Section: Contribution and Outlinementioning

confidence: 99%

“…In this section, we numerically compare the forward models presented above. For the discretization of the partial differential equation, we use the hybridizable discontinuous Galerkin method (HDG), [8,18], and the open-source parallel software hawen, see [14] and footnote 1. It is further employed to carry out the reconstruction with FWI in Section 6.1.…”

Section: Numerical Comparison Of Forward Modelsmentioning

confidence: 99%

“…Furthermore, to avoid the formation of the dense Jacobian, the gradient of the misfit functional is computed using the adjoint-state method, cf. [43,40,3,18]. In Algorithm 1, we further implement a progression in the frequency content, which is common to mitigate the ill-posedness of the nonlinear inverse problem, [5].…”

Section: Reconstruction Using Full Waveform Inversionmentioning

confidence: 99%

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Diffraction Tomography, Fourier Reconstruction, and Full Waveform Inversion

Faucher¹,

Kirisits²,

Quellmalz³

et al. 2021

Preprint

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In this paper, we study the mathematical imaging problem of diffraction tomography (DT), which is an inverse scattering technique used to find material properties of an object by illuminating it with probing waves and recording the scattered waves. Conventional DT relies on the Fourier diffraction theorem, which is applicable under the condition of weak scattering. However, if the object has high contrasts or is too large compared to the wavelength, it tends to produce multiple scattering, which complicates the reconstruction. We give a survey on diffraction tomography and compare the reconstruction of low and high contrast objects. We also implement and compare the reconstruction using the full waveform inversion method which, contrary to the Born and Rytov approximations, works with the total field and is more robust to multiple scattering.

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Section: Contribution and Outlinementioning

confidence: 99%

Section: Numerical Comparison Of Forward Modelsmentioning

confidence: 99%

Section: Reconstruction Using Full Waveform Inversionmentioning

confidence: 99%

See 1 more Smart Citation

Diffraction Tomography, Fourier Reconstruction, and Full Waveform Inversion

Faucher¹,

Kirisits²,

Quellmalz³

et al. 2021

Preprint

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“…The HDG method is specifically designed for first-order problems as it allows to maintain a small linear system compared to other discretizations, as observed by, e.g., [13,22,10,15]. The implementation follows two levels with first the global system for the numerical trace and then local systems for the volume solution.…”

Section: Numerical Calculation Of the Green's Functionmentioning

confidence: 99%

“…Figure 12 shows the time-distance diagram for C surf (θ, t) where θ =r 1 •r 2 is the angle between the two observation points 648r 1 andr 2 . We first compute C surf (θ, ω) using (4.18) with a frequency h ω = 5 µHz and then apply the inverse Fourier transform using (4.19) with N t = 2 15 . We show the section at θ = 30 • for the different RBC, together with the difference with respect to the reference (using Z DtN ) solution.…”

Section: Radiation Boundary Conditions For Time-distance Diagrammentioning

confidence: 99%

Efficient and Accurate Algorithm for the Full Modal Green's Kernel of the Scalar Wave Equation in Helioseismology

Barucq¹,

Faucher²,

Fournier³

et al. 2020

SIAM J. Appl. Math.

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In this work, we provide an algorithm to compute efficiently and accurately the full outgoing modal Green's kernel for the scalar wave equation in local helioseismology under spherical symmetry. Due to the high computational cost of a full Green's function, current helioseismic studies only use its values at a single depth. However, a more realistic modelisation of the helioseismic products (cross-covariance and power spectrum) requires the full Green's kernel. In the classical approach, the Dirac source is discretized and one simulation gives the Green's function on a line. Here, we propose a two-step algorithm which, with two simulations, provides the full kernel on the domain. Moreover, our method is more accurate as the singularity of the solution due to the Dirac source is described exactly. In addition, it is coupled with the exact Dirichlet-to-Neumann boundary condition, providing optimal accuracy in approximating the outgoing Green's kernel, which we demonstrate in our experiments. In addition, we show that high-frequency approximations of the nonlocal radiation boundary conditions can represent accurately the helioseismic products.

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