Isotropic Riemann Solver for a Nonconformal Discontinuous Galerkin Pseudospectral Time-Domain Algorithm

Zhan, Qiwei; Ren, Qiang; Sun, Qingtao; Chen, Hua; Liu, Qing

doi:10.1109/tgrs.2016.2621124

Cited by 48 publications

(8 citation statements)

References 24 publications

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“…Figure C shows the detected signal profiles simulated by Wavenology EL. We validated the Wavenology EL result with that obtained by a discontinuous Galerkin pseudospectral time‐domain (DG‐PSTD) algorithm, which is a well‐established finite element software . The relative mean square (RMS) error between the two simulation systems is less than 2.9%, showing the high accuracy of Wavenology EL.…”

Section: Forward Model On a Digital Mouse Skullmentioning

confidence: 84%

Impacts of the murine skull on high‐frequency transcranial photoacoustic brain imaging

Liang

Liu

Zhan

et al. 2019

Journal of Biophotonics

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Non‐invasive photoacoustic tomography (PAT) of mouse brains with intact skulls has been a challenge due to the skull's strong acoustic attenuation, aberration, and reverberation, especially in the high‐frequency range (>15 MHz). In this paper, we systematically investigated the impacts of the murine skull on the photoacoustic wave propagation and on the PAT image reconstruction. We studied the photoacoustic acoustic wave aberration due to the acoustic impedance mismatch at the skull boundaries and the mode conversion between the longitudinal wave and shear wave. The wave's reverberation within the skull was investigated for both longitudinal and shear modes. In the inverse process, we reconstructed the transcranial photoacoustic computed tomography (PACT) and photoacoustic microscopy (PAM) images of a point target enclosed by the mouse skull, showing the skull's different impacts on both modalities. Finally, we experimentally validated the simulations by imaging an in vitro mouse skull phantom using representative transcranial PAM and PACT systems. The experimental results agreed well with the simulations and confirmed the accuracy of our forward and inverse models. We expect that our results will provide better understanding of the impacts of the murine skull on transcranial photoacoustic brain imaging and pave the ways for future technical improvements.

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Section: Forward Model On a Digital Mouse Skullmentioning

confidence: 84%

Impacts of the murine skull on high‐frequency transcranial photoacoustic brain imaging

Liang

Liu

Zhan

et al. 2019

Journal of Biophotonics

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“…Taking insight from solving the Riemann problem in the localized coordinates [21,35,45,[51][52][53], the eigenvalue diagonalization can be used to solve the fundamental solution for (6.5). For a matrix A, either symmetric or non-symmetric, either Hermitian or non-Hermitian, either complex or real, we have AR = RΛ, (7.1) where R and Λ are, respectively, the right-eigenvector and eigenvalue matrices, assembled in a column manner.…”

Section: Eigenvector Diagonalizationmentioning

confidence: 99%

“…which can be easily calculated by applying the Gaussian quadrature rules [51]. Note that for the zero-eigenvalue inverse in Λ, we just let it be zero.…”

Section: (C) Green's Function In Matrix Formmentioning

confidence: 99%

“…Second, we take full advantage of the Radon transform, by transforming the original three-dimensional space differential equation into a one-dimensional system in local coordinates [50]. Third, inspired by previous work on the characteristic analysis of hyperbolic equations [21,35,45,[51][52][53], the eigenvector diagonalization strategy is adopted to decouple the components of a vector into separate scalar equations. Consequently, a closedform of Green's function is succinctly expressed as a circumferential integral and a spherical integral, corresponding to static and transient responses, respectively.…”

Section: Introductionmentioning

confidence: 99%

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Green's function for anisotropic dispersive poroelastic media based on the Radon transform and eigenvector diagonalization

et al. 2019

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A compact Green's function for general dispersive anisotropic poroelastic media in a full-frequency regime is presented for the first time. First, starting in a frequency domain, the anisotropic dispersion is exactly incorporated into the constitutive relationship, thus avoiding fractional derivatives in a time domain. Then, based on the Radon transform, the original three-dimensional differential equation is effectively reduced to a one-dimensional system in space. Furthermore, inspired by the strategy adopted in the characteristic analysis of hyperbolic equations, the eigenvector diagonalization method is applied to decouple the one-dimensional vector problem into several independent scalar equations. Consequently, the fundamental solutions are easily obtained. A further derivation shows that Green's function can be decomposed into circumferential and spherical integrals, corresponding to static and transient responses, respectively. The procedures shown in this study are also compatible with other pertinent multi-physics coupling problems, such as piezoelectric, magneto-electro-elastic and thermo-elastic materials. Finally, the verifications and validations with existing analytical solutions and numerical solvers corroborate the correctness of the proposed Green's function.

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“…The main methods of forward modeling are the finite difference method [6] and the finite-element (FE) method. [14,15] The FE method can use flexible discrete models with non-matching meshes [16,17] or matching meshes. There is no stable solution for the adaptive refinement of nonmatching meshes, therefore we choose the matching meshes to discrete models.…”

Section: Introductionmentioning

confidence: 99%

A Hybrid Grid‐Based Finite‐Element Approach For 3D Steel Casing Forward Modeling

Gao

et al. 2021

Advcd Theory and Sims

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Steel casing forward modeling often requires considering the slender casing in the study area to study the influence of this casing on the underground electromagnetic field, which can be implemented by the unstructured finite-element (FE) method based on tetrahedra. However, the calculation efficiency of applying the unstructured FE method directly to the steel casing model is poor. To this end, this article develops an FE approach based on a hybrid grid by using slender prismatic elements to mesh the steel casing area, while the remaining areas are still discretely meshed with tetrahedra. By showing numerical examples of the vertical single steel casing and L-shaped steel casing models, the advantages of the method are tested by evaluating the response curves and the degrees of freedom. The results show that prismatic elements are suitable for discretizing steel casing areas. This approach can maintain the high accuracy of the numerical solution and reduce the number of elements required for discretizing the steel casing area. Hybrid grids can greatly increase the computational efficiency of the FE method for steel casing forward modeling.

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Isotropic Riemann Solver for a Nonconformal Discontinuous Galerkin Pseudospectral Time-Domain Algorithm

Cited by 48 publications

References 24 publications

Impacts of the murine skull on high‐frequency transcranial photoacoustic brain imaging

Impacts of the murine skull on high‐frequency transcranial photoacoustic brain imaging

Green's function for anisotropic dispersive poroelastic media based on the Radon transform and eigenvector diagonalization

A Hybrid Grid‐Based Finite‐Element Approach For 3D Steel Casing Forward Modeling

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